The connector has no power to the right or left turn/brake lights. There is power for the tail lights. Anyone have a guide to the relevant fuses and relays? Any suggestions?

 

Owner's manual.

 

If you have a test light check in the fuse block under the hood. Pretty simple just touch the top of the fuses until you find the one thats blown. If you can see in between them with a light you should be able to tell which one isint working.

 

It's a lot faster to look in the owner's manual to see which fuse is involved and then go check it than to screw with ever fuse in the box and hope to get lucky.

 

No Joy Fuses are all good.

Is there a relay or diode or other component in the line that could prevent the trailer turn lights from operating when the vehicle turn signals are working?

 

We don't even know what to suggest since you didn't explicitly identify your vehicle. There were at least three variations in the trailer circuitry between 97 and 03.

 

Check fuse # 36 in the dash panel.

 

1 lesson that I learned. The diagram for the 03 150 shown in the original owners manual is oriented and labeled differently than is the diagram etched in the inside cover of the fuse block.