On my 1999 Cadillac DeVille I replaced the brake switch but still have a problem, could there be a broken wire?
Check the brake light, if it is always on its plunger is not seated down. Cadillac models have a rubber stopper that allows the switch to close completely
A brake light switch fell out of its socket which set a code for the transmission brake light on.
In this case the brake light was always on, what happen is the rubber stopper was missing, reinstalling the missing piece fixed the problem
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