ZDoom

This is a small mod which shows small radar on your HUD. It can detect enemies, projectiles, items and show them with different colors
It has 2 modes, which can be toggled by button (configure it in menu)
Requies GZDoom 1.5.6 or ZDoom svn r2532+
Screenshot:

Neat! I can imagine this would be useful for a Marathon TC.

Methinks Tragos and co. would find it handy, too.

Could there perhaps be a version that only shows enemies if they're moving?

Yes, i uploaded new version with this function(toggle it with button) and ACS source