I'm not seeing the option to do so despite controlling a holy site. I'm not zealous nor a religious head. Is this mechanic disabled or am I missing something?
Right, but it's not the same thing.I don't have your answer but you can convert to the local county's religion by interacting from count emblem and take the decision, if you wish.
This is how it looks like in vanilla. https://ck2.paradoxwikis.com/images/c/cf/Secretly-convert-jerusalem-holy-sites.jpgI am not sure what you suggest is even possible. I might be wrong. Which gives me an interesting idea, but that is another topic...