Ok, maybe I can help clear this up a little (I hope).
The short answer is that the problem most likely lies in the "turn signal/flasher" module, which according to the wiring diagram is located in the instrument panel fuse block.
The module will look a like this:
Now, the long answer. Let's start with the standard 7 pin trailer socket:
As you can see by the diagram, we have 7 connections:
The center pin is for backup lighting
Pin 1 is ground
Pin 2 is the electric brake circuit
Pin 3 is your tail and running lights
Pin 4 is 12V for battery charging purposes
Pin 5 is the Left Turn/Brake Lamp
Pin 6 is the Right Turn/Brake Lamp
Since we're talking lighting we're interested in Pins 3, 5 and 6.
Pin 3, the tail/running lights will be energized any time the parking lights or headlights of the tow vehicle are on.
Pin 5 will be energized (flashing) any time the left turn signal is on or the 4-way flashers are on. It will also be energized (steady) when the brake pedal is depressed.
Pin 6 will be energized (flashing) any time the right turn signal is on or the 4-way flashers are on. It will also be energized (steady) when the brake pedal is depressed.
As you can see, there is no seperate circuit to illuminate the brake lights themselves. The brake lights are run by the same wires used to drive the turn signal. This is done because they are actually the same bulb.
The lightbulbs used in the taillights of our trailers have dual filaments. One (the less bright filament) is connected to the tail/running light circuit. The second filament (the brighter one) is connected to the left or right turn circuit, depending on the side of the trailer it is located on.
This is also why the simplest trailer connection (the 4 pin flat) has only four pins - Ground, Left Turn, Right Turn, and Tail/Running.
In the old days (like up to about 10 years ago), vehicle wiring was still relatively simple, and most domestic vehicles used the same shared turn/stop wiring that trailers still do. Back then, it was real easy to add trailer lighting provisions to a vehicle that didn't come with them.
Those days are gone now, and vehicle wiring has become a bit more complicated. Many vehicles now have amber colored turn signals in the rear, seperate from the brake light circuit (imports have done this forever it seems). Additionally, we now have all kinds of modules and computers to run not only the powetrain, but the radio, windows, and lighting as well (so called "body control modules"). Instead of an electromechanical flasher (with a $3 price tag) to run the turn signals, we now have a module (in some vehicles, a "computer") to do the same job.
Anyway, here's the relevant section of the wiring diagram for an 04 Silverado (sorry it's large, any smaller it becomes impossible to read):
The section we are interested in starts up top, dead center. The dashed-line box represents the "turn signal/flasher module" which is a "fancy" device used to flash the turn signals for both the vehicle and a trailer. Although it performs a similar function in the end, this is not to be confused with the cylindrical 2-pin electromechanical flashers that were used previously. This device has approximately 10 pins and is a solid-state device, with the exception of some relays used to handle current.
I'm not sure if this will help clear things up, but if not, please feel free to comment/question/etc.
- Frank
Sorry. 
H'mm you must also have that same stack of 6" of books in the basement.... as that wiring diagram sure looks like the one in them. 
Linear Mode
