I'm pretty sure Showmap false (or true) will work during your mission, cos I already tried that before in one of my own.
You were an artillery observer in the trenches and you had to click the map to execute a firemission,
The map was only visible when were close to a table with map.
On top of that table, a small (repeatable) rectangle trigger
Activation : Your side, in my case it was WEST
condition : player in thislist
onactivation : showmap true
On deactivation : showmap false
Once you enter the triggerarea your map become visible and when you leave the area, the map disappeared again
Now I'm sure you can do the same thing with ShowGPS, ShowWatch,ShowCompas,ShowRadio or ShowPad
Simply put ShowGPS true in a trigger, script,...whatever