RT1,
I just went through this exact same thing on my 54 3100 (12 V). 1 dim, 1 bright . . . We did every complicated thing we could to make it work. Replaced the socket, got mad, threw tools, argued with each other (husband, dad, sister, and me).
No surprise - It was a ground problem. We just got so frustrated with it, we didn't slow down and trace each wire from front to back. Found a worn ground eventually. Felt like a dope. Hopefully, yours will be solved so simply.
You said that all three sockets have power. Are you using a voltage meter? If so, are you getting full power?
Let us know how it goes and good luck.
