MY 1978 24' Chevy P30 Barth had a Hopkins Style (round) 4-pin trailer wiring connector on it when I bought it (I am not sure if this came from the factory. I did install a fresh connector since the old one was corroded etc. After testing it out with a multimeter I found a potential issue.

These 4 pin plugs (flat or round) have:
1. Running lights (12v/ON when chassis lights are turned on)
2. Left turn signal/brake
3. Right turn signal/brake
4. Ground

I found everything to work fine except when the left turn signal is active, the right turn/brake pin reads 12v. If I am understanding trailer wiring right, this should be off/0v when the left is flashing (which is how it works in reverse when I use the right turn signal).

This only occurs when the chassis lights are ON, and the right turn signal pin reads 0v/off only when the left turn signal is activated, not when no turn signals are on. Very perplexing and I am usually good at deducing what's going on with electrical gremlins but I am frankly not sure where to start on this one.

Ah yes, the magical world of electrons...

Given the age of the unit, I usually suspect poor connections. In the case of crossover power in the lights, be sure that the connections to all the light bulb sockets are good. If you have a bad ground in a socket, the power through the one light bulb filament may not be able to find ground and feeds back through the other filament. Try removing all the turn signal bulbs (front and rear) and check the plug then. The running light power may be back feeding to the brake/turn circuit.

The turn signal switch is the master control. In normal mode, there is power fed through to both brakes when the brake switch is on. When turning, the turn signal switch disconnects the direct power to the brake light and feeds it to the signal flasher to wink the light.

good luck with the circuits...

Be sure and check all the grounds . Bad grounds bring out the Gremlins