Headlight switch

A switch will not cause fuses to blow. If it has bad contacts, which is an open circuit, no current will flow to the affected circuit, so that circuit will be dead, but no blown fuse. If a switch were to short, which basically means it is stuck turned on, the circuit would simply turn on when you don't want it to. There is no other defect causing current to be too high, so no blown fuse.

What you are describing is a short somewhere else in the circuit. For a tail light problem, look first for chewed up wires going to a trailer connector, and mangled wires in the trunk.

We do not have time to follow wires until something directs us to that. Here is a copy of a better approach:

A simple trick to finding a short is to replace the blown fuse with a pair of spade terminals, then use small jumper wires to connect them to a 12 volt light bulb. A brake light bulb works well. When the circuit is live and the short is present, the bulb will be full brightness and hot so be sure it is not laying on the carpet or against a plastic door panel. Now you can unplug electrical connectors and move things around to see what makes the short go away. When it does, the bulb will get dim or go out.

For intermittent problems like yours the bulb may be dim already. Watch what takes place when it gets bright. That is when the short is occurring. It could be due to the rocking of the engine when you shift between reverse and drive. It could be due to the body flexing when you drive over bumps in the road. The bulb limits current to a safe value when the short occurs, in this case about one amp.