Here's a wiring diagram of the 7-way connector. Since it's affecting stop lights, right turn and tail lights, it's more than one pin (Pins 3&6).
Since you have tail lights on the left side, and not the right side, I wouldn't believe the issue is with your 7-way because the tail lights for both sides are on pin 3.
My suspicion is that your right side bulb is burned out or you have a bad connection between the trailer wiring and the right side light housing. I'd start by putting the left side light on the right side. If it works on the right side, you'll know it was the bulb. If it doesn't work, pull the right side lamp fixture and check for connection issues.
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