Rick,
The delay is built into the processor that mounts under your dash (or similar location). The small push button is just a transmitter to that processor.
You can't control the exhaust brake directly through a push-pull switch. The way it works is this (assuming you have already turned the brake ON, and that the self-test is completed):
When you push the button, the processor is commanded to close. The processor waits about two seconds and then commands the pull relay and the hold relay to energize their respective coils at the brake. After about one or two seconds, the pull coil is commanded to de-energize, leaving the hold coil to keep the brake closed.
When you push the button a second time, the processor again waits a second or two and then commands the hold relay to de-energize. This turns off all power to the coils at the brake and the spring opens the brake.
The pull coil draws about 40 amps and must not be energized for longer than the one or two seconds that the processor is set up for or it will overheat. This current draw is more than even 10 gauge wire is rated for, so the wire will also overheat. Eventually, if the pull relay (and coil) remains on with its 40 amp draw, the automatic-reset circuit breaker in the system will trip, saving you from setting your truck on fire. This will de-energize the exhaust brake, causing it to open and removing any engine braking that you were depending on at the time.
If you don't select the brake to OFF, the circuit breaker will automatically reset after a delay for cooling and the exhaust brake will close again. Then it will trip the breaker and open, etc.
This is a confusing problem to diagnose, but if your U. S. Gear brake is cycling on and off by itself, that is probably what is happening.
The bottom line is that you must use the processor (controller) that is provided with the system for it to work properly. There may be a way to signal the processor with a push-pull switch rather than the push button, but U. S. Gear doesn't publish how to do that with their instructions.
One last thing: If you use the push button, tape it in place where you want it before you mount it permanently. This will allow you to check for a good signal to the processor before you permanently install it. Some locations on your truck may not provide a reliable signal to the processor.
Good luck with it.
Loren