How much time between quick attacks when attacking gym?

That depends on who you're attacking and their moves. You should be able to use Zen Headbutt 2-3 times against many Pokémon with slower fast attacks. With slower fast attacks being ideal for defending, that's what you should prepare for when going into a fight. In general, the faster your fast attack is the easier it is to dodge while damaging the enemy. There are a few exceptions in certain situations like what you pointed out that you might be able to use either of the moves once but not twice, and that could actually make Confusion theoretically better. In most cases however this is not the case and that's probably not how you should optimize your Pokémon.

Its not possible to use zen headbutt 3 times even against the slowest moves like bubble and confusion. 2 isnt possible consistently neither at least not with consecutive successful dodges.
The answer to the question depends on the move your using and the move of the defender. Some defensive moves are slow so you can squeeze more attacks in and other moves are fast so you must attack less. I fight ALOT in gyms...
For example against Dragonite's with WA and a Dragonite's with DB I can squeeze 3 frost breath in on a wing attack and only 2 consistently on DB. Using my Dragonite with DB/DC I can get 7 attacks in on a WA and 5(maybe 6 sometimes) attacks on DB. So it depends on both quick moves. I classify quick attacks into three categories on both def and offense and each category will allow a different amount of attacks in between successful dodges.
Whats even more interesting is I can squeeze in a DC between succesfully dodged WA's while DB will catch me before I can dodge.
If you like my answer pls give me a thumbs up. OK two thumbs down I wont share anymore lol