My 1988 Ford Bronco’s right turn signal quit automatically blinking a month or two ago and burns constantly instead when activated (the light can still be operated by flicking the shaft from off to full burn back and forth). Since then the left blinker has done the same thing, and now the rear lamps don’t light when the brakes are applied, only when the car is in reverse. I have replaced all the fuses and the turn signal switch, all to no avail. What could be causing the problem?
Try replacing the lamp. If I am right it has a duel use bulb where there are two filaments in it. Often one filament will sag and make contract with the other causing this problem. Cheap easy fix.
Now after reading the rest of your message, I will add a second likely issue. Make sure you are getting a good ground, often trunk or hatch mounted lamps share a common ground, that ground wire may be defective do to years of flexing every time the hatch/trunk was opened and closed.
Odds are that the turn signals & emergency flashers use the same bulbs/grounds& wiring & the only difference in the 2 circuits is in the turn signal/multifunction switch (which you allready replaced) & the emergency flashers will use a seperate flasher.
Do the emergency flashers work?
If not you need to do as Joseph suggested & check for a ground problem.
Also check for voltage at the bulb sockets.