The I would check the multi-switch.
You can start at the back and remove both bulbs, use OHM meter between the two turn signal contacts with key off turn signal off.
Should be high ohms,
if not then either the wires or multi-switch has a short between these wires, disconnect multi-switch plug and test again, if short goes away then replace multi-switch.
If short is still there with multi switch disconnected then you need to start tracing the wires, start at the back and work you way forward, unplug any connectors and retest as you go.
If there was high OHMs on the first test then turn muli-switch to right hand turn, key off
test OHMs again if ohms are low then replace multi-switch.
You haven't said yet if you have a trailer light connector, these are often the source of these type of issues.
There is no trailer light connector on my 90 Ranger..
I've already tried using a good working turn signal switch from my 89 Ranger and put in my 90 Ranger to see if that would correct the issue of both rear turn signals blinking in my 90 Ranger, but it didn't help..
I also tried removing the bulb on the Right front and Right rear turn signal socket and turned on the right turn signal switch, and the left rear turn signal bulb still flashes..
I even tried running a temporary ground wire from the negative battery post to the right rear turn signal light bulb socket when the bulb was installed, and both rear turn signal lights still flash..
I also cut off the right rear 3 wire turn signal socket and the left rear turn signal light still flashes..
When I put on the brakes, when the ignition switch is on, the rear turn signal lights will stop flashing and the right front turn signal light will stop flashing for as long as I'm depressing the brake pedal..
Even when the ignition switch is turned off, the passenger side front turn signal will light up, when the right turn signal switch is on, for as long as the brake pedal is being depressed..
I'm almost temped to cut off the passenger side front turn signal socket, (in case it's a bad socket), and see if that's the cause of my rear turn signals not working properly.
After doing some online searches for trying to find out the possible causes of both rear turn signals blinking on a vehicle..
I discovered that one possible cause for this happening, according to some peoples' experiences with this problem, is when a front turn signal bulb socket is shorting out, it can cause both rear turn signal lights to flash..
Does that sound possible?