There are quite a few sphinx moths that use members of the grape family as host plants. I think just about all the the Eumorphas use grape family vines/plants, also Abbott's sphinx/Sphecodina abbottii, Lettered sphinx/Deidamia inscripta, Nessus sphinx/Amphion floridensis, and Hog Sphinx/Darapsa myron. They all make cute moths. I don't know which, if any, of them lay their eggs in large groups like yours did, so your eggs may not be sphinx moths, but it's a start.
I've included a link to a list of sphinx moths of America. You can click on each one to find a lot of information about each type. I'd scroll down and start on Eumorpha if I were you.
If, after the eggs hatch, they have horns on their rear ends, you know they're sphinx moths.
Sherry

Here is a link that might be useful: Sphinx Moths of America

I don't think that they are eggs at all, but something that the plant is exuding. The first clue to that, in my mind, is that the 'eggs' (droplets) are all located on or very close to a primary or secondary vascular vein.

I've seen this particular type of exudation on other kinds of plants, mostly those with calcium oxylate crystals in their sap. Which this plant contains, by the way.

What do you think of this theory?

Wow! I love this forum---thanks for your input, misssherry and rhizo. I'll keep you posted on the outcome.
regards,
seedmoney