Well, if V2 is giving us the green light to bluff him off JJ/QQ, or AQ, then let's just shove. Trusting that you are right about V1. If we can make V2 make an incorrect fold against us, let's do it. This is pretty much a physical tell/feel thing though. I would only do it against players I know.
I once had this exact situation happen when I had TT on the button. A tilting player bet, I called on the button with TT, and an old TAG 3-bet from the blinds, the tilting player raised, the old TAG wasn't acting too strong or intense so I reraised all-in, and the old TAG made what looked like a "standard" fold. The board came J high and the old TAG groaned that he would have made a set. The board came with no ace/straight, I flipped over my TT at the end and the other guy flips over...AT! Everyone was shocked
.
This situation is a little different positionally, but the dynamic is the same. If we know this guy will reliably fold whatever he has when he acts like this, it arr-in time.
If he were being really hammy about it, I would assume he has the nuts. Various regs at my casino would sigh, shake their head, and say "all-in" when they have aces.