Yes the nymphs do usually cluster together--but they are fast when discovered.

I went all through the garden yesterday, checking each cucurbit leaf, picking off all the eggs and wiping the nymphs and adults into the jar of soapy water that I had. All went well until the last plant when I kicked over the jar, releasing all the eggs, nymphs, and adults to the ground. The adults and the nymths all seemed to have drowned, but I came back with some neem oil to hopefully finish them off. Does anyone have any thoughts about whether or not the eggs would still be viable?

Those squash eggs are sure tough. I read on here somewhere to pull them off the leaves with duct tape, which worked fairly well.
Bummer that you dropped your jar! Was it somewhere where you could spritz it for awhile with more soap and veg. oil?
Or, if they are dried up now, you could collect them with the duct tape and then hammer on them.
I've been reading about using castile soap spray on them, but haven't found any castile soap locally.

I tried using packing tape last year (I forgot about that this year). I just decided that what little damage I was doing to the leaves was much less than what the bugs would do if I left the eggs alone.

Unfortunately the jar was spilled right in the middle of the plant. To try to do anything about the eggs whould have upset the vines.

Maybe the birds got a treat. If not, I guess that I'll get another shot at them when they become nympths.