I have no sources, neither have I much experience, but as it seems to not be welcomed to have partial answers in comments, here I go with an answer:
I suggest you rule this by situation. If the player tries to intimidate somebody by doing something that could show where he is, e.g. making a noise, roll for the target's perception with a fittingly hard or easy DC.
I wouldn't rule in this case that the invisibility ends, but the enemies are temporarily aware of the approximated location if they roll high enough.
It seems like the 5e PHB would not even let them make a roll - but this is not the edition you asked for and I don't have the pathfinder one at hand.
An invisible creature is impossible to see without the aid of magic or a special sense. For
the purpose of hiding, the creature is heavily obscured. The
creature’s location can be detected by any noise it makes or any
tracks it leaves.
(PHB p. 291, Conditions)