It sounds like this has nothing to do with the trailer brakes or the brake controller.
You should ALWAYS flush out all old brake fluid every time you work on the brakes. Read you manual, it probably recommends every two years or so. Brake fluid is hygroscopic and absorbs water from the air right through the rubber lines.
The master cylinder certainly could be bad.
Keep in mind this is a 16 year old vehicle. The rubber lines are likely shot if never replaced. A rubber line can collapse causing pressure to remain in the caliper and cause the brakes to drag. If your brakes are dragging they will heat up and stink. Even if the rubber lines look good on the outside, replace them.