Problem Solved!
Just to summarize, none of the turns signals on either side worked and the emergency flashers would not come on, but the parking lamps worked.
There are two fuse boxes for the '94 GT, one in the engine compartment and one inside the car, under the dashboard, just above where your left leg sits.
I was told by several helpful members of StangNet that it would either be a blown fuse, a bad bulb, or the flasher relay box itself. The flasher relay box is a yellow box that sits just behind the interior fuse box and is connected to the fuse box by a slide connect and a plug.
You can rule out a bad flasher relay if both your emergency flashers and your turn signals stopped working as they apparently use different flasher relay boxes. If just the turn signals don't work, you may have a bad bulb or a bad relay. Luckily, for me, it turned out to be a fuse problem and not a bad bulb or the flasher box itself.
The signal/flasher fuse is the "number 1" fuse and is 15amps (light blue). The diagram I had was for a '95 and didn't quite match my '94 fuse box layout, but there were only five fuses that were 15 amp, so I pulled each one and, sure enough, the last fuse that I pulled was blown.
I replaced the blown fuse from the spares in the lid of the fuse box cover and everything works again. Thank you very, very much to "HISSIN50" The Green GT" and "bill302" for taking the time to help me out!
