I recommend that tangle traps break stealth and invis when triggered. Self serving, yes, but it makes little sense for someone to get tangled up and still be able to hide. Maybe alternatively give the person afflicted by the trap a deduction to stealthing skills.
I can see no reason this would ever strip invisibility. And as it has been explained before, stealth is psuedomagical. Else you'd not be able to hide in the middle of the street and not be seen either. If you're watching the trap, you can see when the box goes away, at that point its up to you to figure out how to find them.
Not likely.