NO! The rear brake light is on its own electrical circuit, which is activated by the rear brake pedal.
I will defend Zedx11. He has been a bike mechanic for three years now, and has put together several hundred bikes together out of the crate. No one has ever come back on his work, either for mechanics, or assemblies.
And how many brake lights are we talking about? One, but it can be switched on by one of two sources: the foot brake or the hand brake.
That means there are two SEPARATE circuits with separate switches feeding the brake light bulb (front lever, rear pedal).
If the brake light stops working completely, how likely is it BOTH switched +12V feeds (which are parallel wired to the brake light filament) both failed together?
Ergo, screwing up the foot pedal switch ALONE should never make the brake light stop wirking if activated by the front handlebar switch.
I was relying on the OP's statement of:
it doesnt work when you apply the front or rear brake at this point
that, and 35 years of experience as an electrical engineer, when I said it was more likely the bulb (or fuse) than the pedal switch.