1970: It sounds like your brake switch, or line is making a ground which is allowing those devices to operate. If that is so, follow the brake cable all the way and see if there are any worn wires along the way. If that isn't it, then it could be that when you pull on the brake cable you are also pulling a wire together somewhere which completes a circuit so that those devices will operate. Again, look along the entire brake cable to see if you have any worn or broken wires. And last, it is very possible that you have a bad ground/chassis connection somewhere. If you have a short circuit (where a positive wire is shorted to the chassis), then you'd be blowing fuses, and you're not doing that. Therefore, it is most likely that you have a bad ground somewhere, and that ground is common to all the devices you listed. Additionally, when you apply the brake, that bad 'ground' is turned into a good 'ground'. Look for loose parts and connections, and bad chassis grounds. And, of course, look for a broken or worn wire along the length of your brake cable. Good luck. This will take some detective work, but I think this information will help you.
USFS Motorized Trail Maintenance Volunteer