Yeah, I also believe it's more likely a connection rubbing inside the headlight bucket but it doesn't really make sense.
If the brake switch triggers the starter solenoid, you would think the starter button would turn on the brake light but no, it doesn't do that. It just turns on the solenoid.
Also, when the brake triggers the solenoid, the brake light doesn't turn on just like when the running light switch triggers the solenoid, the lights don't turn on.
It's working right now but I still replaced the solenoid because of the sticking issue. Starter motor running continuously at 1am was not fun and realizing pulling out all the fuses does nothing.