Have you removed the bulbs to inspect if the filaments are blown?
Is there moisture in the housings, visible from the outside? Bulbs getting wet? Green on the bulb to connector contact areas?
If not, continue below ...
Yes, there is a switch, relay and fuse that can all be suspect but when one light filament goes out, the other usually fails in short order for whatever reason of engineering/physics.
Check the bulbs, if the filaments are burnt/open, replace them both and you are likely back in business.
If filaments are burnt and new bulbs fail to light, you can check for the fuse. Due to burnt filaments, unlikely to have a short, unless someone previous to you, tapped into that circuit.
I don't think we have 2005 Mirage FSM's here, but usually there are fuse layouts in the factory owners manuals, which are either with your car or can be ordered online from Mitsubishi/Ebay or can be downloaded from Mitsubishi (as some OEMs have started doing via PDF files).
You are looking for the FOG LAMP fuse or something of that nature.
Start there, my advice.