Look like the same problem a lot of 87-93 GT owner have already had.
The fuses is the first thing to take a look but it's rarely this.
Other problem can be about the fog light. The factory wiring gauge is not enough big then it start to give you problem with the headlight. Mine start blinking and i fixed it before it completly shut.
Here's the solve
Fog light fixing on Mustangworks.com
When you'll remove the switch, take a look on the connector if it look like heated. If so, here's probalby your problem.
Hope this help