not many people wick them - at least i haven't seen any post s here.
i actually wick a lot of plants since i started wicking my AVs a few years back . begonias seems to be a natural choice - being quite similar to AVs.
i cut av soil with perlite to make up close to 50% perlite (av soil contains some already). and i set up wicks to drop into water containers.
at present i only have reiger actively on wicks. but i have planted non-stops with wicking in mind and am going to take them in once the temps are below 40s at nite.
which will be coming soon.
i read that they will continue to flower/be active for a couple of months after you bring them in. beyond that i don't know. i actually want to keep them going longer to see if they have set/developed tubers. i did dig up one of them that declined back in sep - it had a little tuber already going.
my understanding is that if tubers are small and they go dormant - there's little chance that they will be able to wake up. to key to keeping them going is warmth at the roots and sufficient light.
i have one large tuberous still going strong outside - i think it can take low 40s Ok. then i'll bring it in for a few months and let it do dormant by jan.
i think that large tuberous need 2-3 mo dormancy.
non-stops don't know - not much info on that.
what kind of begonias are you keeping?
i have a good light in western window and i don't do lights ... yet.
but if you look at some posts - you can find some info on lights too.
unfortunately it's not a very active forum here. you might have better luck growing under lights or even hydroponics - though they don't discuss wicking that much. the only wicking people here are AV people. but then they don't wick anything else much
i wick all sorts of plants: ficuses, caladiums, ferns, aralias, philos and aroids.
but i am not very experienced with begonias, just playing.

I only grow six months out of the year under lights - all are 2 tube T12 and T8. For tall plants (canes mostly) I may hang two lights (for a total of four tubes). Most do very good with this setup. I don't wick at all. I use drip trays so what water is left in the tray will in effect be wicking. There are some species or hybrids that need terrariums to do their best but most are comfortable in trays under lights for winter and most grow as well as outdoors. The terrariums stay indoors all year but they may not get water for months and this can be a problem in itself (just because they are in a semi-sealed environment does not mean that water will always be there).

The one thing about rexes is they do not need as much light as you think. A simple shop light is often enough. My daughter had a rex in her kitchen with very little light and very little care for a couple of years or more and it was unbelievable.

I wick begonias, always have. Currently I have B. sillentensis on wicking as well as Bs. leathermaniae and aconitifolia and 'Seabird', these are the largest, I also do a lot of cuttings by 'Texas Style' wicking, that works so well many times the propped cuttings have grown a great deal more than I wanted and I have to force them out of the one cup styrofoam growing medium. OUtdoors in summer I have to wick many of my tuberus species, or once they dry out they are gone.

Great advice and I am happy to hear that the begonias are easier to please, then I thought. I enjoy them, so much. I noticed a lot of the rex and rhizomatous begonias are doing fine, in what I thought was less than enough light. All are under at least a 2 tube, T12, light.
I have heard so many people say that rexes only do well for them in almost full, morning sun. They commented especially on 'Escargot', as needing almost full sun. I have 'Chocolate Cream' and it is happy at the corner of a 6 tube, T8 stand. I have had it for several months.
I treat them like violets, with the most patterned and darker leaves getting the best light and species and less patterned ones, to the ends of the stand. I have a couple, like B. chlorosticta red and B.brevimorosa, that brown, on the edges, but B. chlorosticta green form, and other species, such as masoniana, paulensis, luxurians, and microsperma, are all fine. I am not sure whay this would be so, when the humidity is about 80%, at all times. I have tried the chloristicta red, under cover, with not better results. B. brevimorosa is newer, so I am trying it under cover, to see if it gets going, then I will slowly acclimate it to room air.

My chlorosticta is feeble but then I have so many other nice begonias that if it kicks the bucket it won't be missed. My paulensis did wonderful last winter in its original pot to the point of being a hog (water and space). Then I potted it up and moved it outside where it dwindled next to nothing. Lessons learned - keep this one indoors but I don't like to cater to plants indoors during summer. I find brevirimosa a difficult one indoors - wonderful outdoors so I've given up on it for now. Luxurians is another challenge but I've got the same one starting its 3rd winter - I suppose I was under-watering the earlier ones in winter. Not that attractive a plant but it is a conversation piece.

Escargot is one of the most notorious begonias to grow. Another great one outdoors but indoors it sulks and finally kicks the bucket. I do have one in a good sized terrarium which is doing good (not great like the ones I have had outside). I think most folks starting out with this one will sour on begonias if they thought this was the norm.

What is it about outdoors, that you feel makes the difference? Is it the amount of light, heat, or humidity? I have almost have outdoor conditions, as far as light and humidity. I have a light meter and the 6 tube T8 fixtures, come with a reflector and put out 30,000 lumens, nearest the bulbs. That means the plants under them, get around 18,000 lumens; a bit more than bright shade.
I don't want to deal with bring plants in and out. I have a hard time keeping thrips out of the indoor collection, without bringing plants in, from outdoors. I am hoping that replacing many of the violets with begonias, will cut down on the thrips. Violets ( I have over 200 varieties) are thrips magnets. I really want to grow begonias, of all types, to perfection, indoors. I really enjoy the challenges and camaraderie of showing plants and being part of a plant club.
I have several canes, as well. They were by favorite begonias to see, growing up. I always wanted a large-leaved, nicely spotted, angel winged, begonia. I have 'Cracklin Rosie', 'Good n Plenty', B. maculata whiteii, and a few others. I think my most happy begonia, at the moment, is 'Pink Minx'. It looks like someone colored it in, with a glitter gel pen. It is truly amazing, the colors and reflectiveness, you see, in the many types of leaves.
Once I get growing, I'd like to try hybridizing, perhaps to get a miniature, curl-leaved, begonia, with fantastic coloration. I am thinking a Begonia 'Five n Dime', with the curl of 'Super Curl' and truly tiny ones, with colors, like 'Fire Works'. I need to look into information about dominant and recessive traits.

I think you will be fine growing most begonias indoors. There are a few though that just need more humidity and a terrarium is usually called for. I really don't think light is a big issue. I've grown tall canes under an ordinary shop light and can get blooms (not as pretty or as heavy as growing outdoors though). My mentor grows/grew hundreds of varieties of begonias and gesneriads indoors but they were all in terrariums. If the begonia got too large she would snip a leaf and start it anew and give the big plant to her husband so he could 1) plant it in the ground to give away in fall and/or 2) keep it in his small greenhouse. I sure didn't want to have all terrariums even if all her plants were in pristine condition.

The reason I move them in and out (a huge undertaking often taking a couple of weeks or more) is in summer I switch gears to gardening outdoors and the begonias become part of the landscape under tall trees and help fill voids while azaleas, Japanese maples, hostas, and hydrangeas are filling in. I can kill two birds with one stone by watering, grooming, fertilizing, etc. It becomes a win-win situation in my book.

Here is a small sample.

What a beautiful display! I would like to know what the center two plants are called. They are beautiful! one day soon, I'll post my growing list, but just the begonias; not the 100s of violets and gesneriads, Hoyas, and carnivorous plants, or the stapelia....lol I'm a hopeless addict.

B. soli-mutata is the dark green one with light green midsection and Benitochiba is the pink/white palmate one.

I don't think you are the only addict here.

Here is Connee (sometimes spelled Connie) Boswell.

I was referring to the one to the left of the soli-mutate. I have the B. benitochiba and it reminds me of Gryphon. I am most enjoying my Pink Minx, hemsleyana, masoniana and its variants, chlorosticta green, and Cracklin Rosie. I have a B.crassipes I also find interesting. I just have so many that have something of merit and they all look like potential parents, for my hybridizing projects, to come. I am in deep!

Oh, the silver one with green edges and center is 'Silver Queen'. Great begonia but come fall it gets full of mildew so all the leaves are gone now - they will be back in no time but I may have to remove those too if it gets too much mildew.

Here it is again with U400, Tangalooma, and one of Steve's Leaves begonias (either Elephant Ear or Old Blue or True Blue or Big Blue - something like that).

My plants go in/out, seasonally, so don't feel like I have any advice, but wanted to say Hi & best of luck!

BradsBegoniaWorld.com has a lot of good information. That is where I started. This is where I am now: http://www.flickr.com/photos/54481051@N05
For potted begonias.I use Pro-Mix and perlite from Lowe's, plus a bit of charcoal. I buy a bag of hardwood charcoal, put a few chunks in an old pillow case, and take a hammer to it

Here is a link that might be useful: My begonias.

Wow! That B. chlorosticta looks great! I acquired a few more begonias, this weekend, at the Mid-Atlantic African Violet Society convention. I have to get my grow list updated. So far, the ones I have are doing great and the ones that were on the mend, have improved, since being potted down and placed in a lighter mix. I learned that the begonias really like it much drier, than my violets. They certainly did not miss my not being home to water them, for 3 days. I know now, to let them ''ask'' for water, before judging, by the appearance, of the top layer of soil.

Yes, very beautifully grown chlorosticta! Great job there.