Other than a short there are two possibilities that can cause the brake lights to stay on.
1) A defective switch that keeps them on.
The test for this is to unplug the switch and if the lights go out you know the problem is not a short in the harness.
Before condemning the switch you need to do step 2
2) It is possible that the brake fluid pressure is not releasing in the master or is releasing very slowly. Since the switch is in the air pack and not on the master you need crack the brake line bleeder at the top of the airpack and if the lights go out the problem is upstream and the master is not allowing fluid to return to the resevoir. This also can cause dragging brakes. If the lights go out when you do this, the switch is ok.
If you determine that the problem is pressure in the master not releasing, check the freeplay of the brake pedal. You should have about 1/16-1/8th inch of freeplay where the adjustment rod enters the master. If there is no play, adjust until there is as I describe.
If the rod is adjusted properly, you may have a plugged relief port in the master. To test for this, open the master cylinder by loosening the breather with 3/8 wrench and then take the cap off with a 3/4 wrench.
Press the brake pedal with your hand and release watching in the resevoir for a return flow of brake fluid. An upwelling should be visible when you release.
Explanation: There are two ports in the master to feed the piston assembly and let the fluid back. The big port is where the master refills the area that the piston uses to pressurize the brake system. The small, even tiny, port is ahead of the main piston seal and allows fluid into the resevoir when the piston is at its rear most position.
One last item is that the airpack itself can be defective and keeping air pressure on the main piston and thereby apply enough pressure to keep the brake lights on, and also the service brakes most times as well.
The first test checks for pressure in the lines and if everything else in the brake system has passed the tests I have described here then you are looking at dealing with the air pack.
I hope this is helpful