It is not uncommon for the brake light switch to fail and cause this. If you're LHD, it's just above the brake pedal. If RHD, it's just above where the brake pedal on a LHD car would be
i.e. on RHD, it's accessible by removing the carpet under the dash below the glove compartment. Then it isn't hard to replace. It's plastic and I don't think oiling it would help.
I've heard people say they took the switch apart and checked it and it seemed to work OK, but failed again when they put it back on.