International 9400 Rear Tail Light

Possibly a rubbed wire or corrosion inside a plug letting voltage through.
@Heavyd

 

I do not know but when you transfer from running and or head lights to turn signals the problem is often where you have a bad or dim light. Does the right tail light wiring junction in the left tail light?
Regardless of any of that disconnect all of the wiring harness plugs you can along the way. If a disconnect stops the turn signal flashing the marker lights you know which way to search.
Often bad grounds but they will not cause a light to stay on.
A more in depth description might help.
Now we have chassis control modules and such but I thank you are bit older than that.

 

What is the last 8 of you VIN?

 

I am suspecting you are getting tail light power shorting to the brake/turn light circuit and this is why it is staying on. Start testing by leaving the lights turned off and only the hazards on. Is the tail light staying on solid with just the hazards on only?

 

For the right turn indicator, if that light is on when you have the brakes pressed, take out the right turn relay. If the light is still on, then something back feeding from the trailer socket feed circuits somewhere. This may affect your tail lights too. For your turn light issue, make sure you have a good ground connection with your lights back there. If they aren't the plain factory lights, and they have been rewired for custom lights, this makes everything even more complicated for obvious reasons. Disconnect the lights one at a time to see if the problem stops. Try switching lights side to side in case one is internally shorting.