X-Plane doesn't natively and directly support popup panels, but that doesn't mean you can't pop them up. Generic instruments have a dataref-driven set of show-hide fields. (The "filters".)
Now what you might not have realized is: groups have filters too! So you can hide an entire group with one filter, and you can put premade instruments in the group.
So...even though the FMS is a premade instrument with no filter fields, by grouping it you can show and hide it.
Important: the backgrounds of instruments are not shown or hidden. So if you want to do this, customize the FMS to have a transparent background, and use a generic rotary to put a real background behind it. The rotary goes in the group, and thus it can show and hide.
One more tip: clicking in 2-d goes through one instrument to another, for historical reasons. So if you pop up an instrument, you might want to hide the instruments it popped up over so clicks don't affect them.