OMG, you're out of blinker fluid!! ha ha, sorry......ok....You can buy a bit set at Checker/schucks/Cragen for under 10 bucks that has like 4 different sized tamperproofs in it.
Same thing happened to me, a flasher is like $3, if you remove your hazard flasher and plug it into the turn signal harness you'll know if thats the problem without spending money. If its factory stock it should be on the passenger side underneath the dash, its light blue and has a fastener on it to hook into the dash. If you have a mustang repair manual it should give you the same directions to locate it.
First remove those panels around the steering wheel, and make sure the wiring to the multifunction switch is all there. There's a light blue wire that plugs in to it which runs from your turn signal relay to the switch.. mine came unplugged, and it took days of troubleshooting to figure it out. Second, if you haven't replaced the ignition switch yet (too lazy to read above,) do it anyways. Replace the relay too.
Is your heater fan cutting out when your signal quit working? I know this sounds stupid, but that's what mine did and it was the ignition switch. If you determine it's not your ignition switch, I'd think seriously about replacing it anyway. They tend to cause lots of freaky electrical problems when they get some age on them. I think there was a recall several years ago. Cars were catching on fire because of the ignition switches going bad. BTW, I was able to clamp some vice grips on the outside of my ignition switch tamperproof bolts and loosen them that way. Good luck!
unfortunatly blinkers ignition and all pwr inside except aux pwr sources run thru the ignition switch, check the turn signal relay, then ignition switch, I reccomend replacing it anyway.
i have had the same problem a couple of times too. first make sure all of the wires are actually in the connector to the hazard switch there should be 7 wires going into the back of the connector if one of them comes loose due to a cracked connector the turn signals wont work... and for the flasher if it has never been moved from the stock location it should be attatched to the metal brace for the dash between the radio and the glove box you just twist it and pull it up off the brace for the dash the easiest way to get to it is take the glove box out... and since you cant figiure out what most things look like... its a light blue cyclinder about an inch tall