trailer brake light problem

I have an 04 Silverado 2500HD with the Duramax and am pulling a very small trailer with camping gear. A buddy (following me) tells me that the left
brake light on the trailer doesn't work. He also tells me that the left and right turn signals work and that the tail lights work. So: The bulb is a double filament and both filaments light when they get power. The bulb is good. The connecting wire is also good since both circuits light.
The trailer has a flat-4 connector which is plugged into the truck 7-pin receptacle using the Chevy-supplied 7 to 4 adapter. Tried another one adapter with the same result.
It seems to me that there must be a separate trailer brake light circuit in the truck, maybe with it's own set of circuit breakers, fuses, and solenoids.
Any suggestions? Other than take it to the shop?
Ralph
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you have a Floating Ground on the Left ligt bulb socket ( POOR GROUND) your Break light Circuit is finding a Ground Via the Tail light filiment to The DASH light GROUND or the front parking light GROUNG
REground the left trailer socket.(RUST is the Cause )
Pumper Hinkle wrote:

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Please check the Fuse box under the hood. The 2500HD have seperate feeds and fuses for the back of the truck and the trailer.

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update: Thursday:
Thoroughly checked out both trailer lights with an ohm meter. No shorts or grounds.
And, I found that if I pressed on the brakes and set the 4-way flashers to flash a couple of times, I'd get my brake light back again. Sometimes. Then if I repeated the process I'd lose the brake light (mostly).
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Took it to Chevy, they replaced the multi-function switch under waranty. Works fine now.
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