Turn signals problems are my latest issue. Left side works normal but the right side doesn't blink, they just light up. I tried replacing the corner marker bulbs with new ones as well as the rear tail light bulb. I'm going to install a new one in the front but it does currently work, it's like it has a flasher issue. Are there two flashers, one for each side?
You might need to probe around with a multimeter. If you have access to the official manual then compare with a wiring diagram. The diagram in the Haynes manual is completely wrong for an 86GT, I don't know if it's right for any particular model. Don't put faith in it.
Bad ground can cause this. I had that happen on my car. Same exact symptoms, problem turned out to be a bad connection to ground at the front bulb socket. It would still light up but nothing would blink. I had bought a new socket so I thought the problem was elsewhere. Nope, once I got a correct diagram it narrowed back down to the new socket - it was just as bad as the old one. The ground is in 2 pieces inside the socket. There's the wire from the harness which ends in a metal tab, and then there's another metal tab which leads to the bulb connection. Those metal tabs just touch each other through spring tension. I broke open the socket and soldered those tabs together, epoxied the socket back together, and that was what fixed it.
There is one turn signal flasher. When you flip the switch for left or right, the electricity flowing through the flasher gets shunted to the left or right side turn signal circuit. So you don't have a bad flasher.
Chances are it's a bad turn signal bulb (probably the right front, since you said you checked the rear), or a bad electrical connection somewhere. Considering how old our cars are now, it's possible one of the light sockets has corrosion or gunk inside interfering with the electrical connection.