Did you already looked once at what your browser does when you load a dashboard page? Did you look at what happen when you change the value in a prompt which is going to reload analysis in the page with the new filter?
If you didn't it's maybe time to give it a try ...
What you ask is supported out of the box if you use the embedded map functionalities.
It's also kind of simple if the click would navigate to a different page passing a parameter in the URL, even if you navigate to the same exact page by adding the clicked parameter in the URL.
But if you want to make it without navigation, without reloading the full page, I guess you can plan few weeks of works for a half working solution ...
And of course at each update/upgrade you will have the surprise to discover if your code still works or not as there is no guarantee things will not change.
Have a look at what your browser does when you do something in OBIEE and you probably see why I'm highly suggesting you look for a different behaviour
Thinking out loud here.
Totally crazy and novel idea: Why not use the tool as they are built and go for Visual Analyzer? Shocking to actually use the software you are already paying for, I know...
And if you complain that you don't have VA because you're on 11.1.1.something - well next time include it in your question.