We never 3 bet any hand for "information". We 3 bet becasue either:

A: For value. We are comfortably ahead of their opening range and their 3 bet calling rnage doesn't crush us.

B: As a bluff because their opening range is wide and we expect them to fold often.

Obviously we never use JJ/1010 for a light/bluff 3 bet, so we are either doing this because we're ahead of their range (eg. 20/16 CO opens we have 1010 in BB) or we are electing to call instead because it is ambiguous whether we're ahead of their range or not. (Eg. TAG 17/15 UTG opens and we have JJ in the BB. )

So we don't 3 bet 1010, JJ in certain spots because we are in bad shape OOP vs their 3 bet calling range which might be something like [AK AQs 1010-AA.]

So when we flat these in the blinds we're doing it to gain maximum equity post flop and also try to flop a set. This doesn't mean we're going to c/f a 8 8 2 r board though becasue we didn't flop a set. It means sometimes we may have to c/f bad boards, however, we get to play our hand profitably on favourable boards like the 8 8 2 because we didn't 3 bet and hence left villains range wide enough that we are NOW well ahead of it.

I think if you're 3 betting just for information you need to stop it as its a massive spew.