i had the same problem with one of my fog lights. same exact symptoms. good fuse, good switch, voltage at terminals, but no light. it was a bad ground. doesnt mean thats what yours is but could very well be
I would agree it's a bad ground. I took a quick look at the wiring schematics in the Bentley, and all 3 brake lights ground at the same location. And the brake light switch should be working fine, as it's on the positive side of the circuit and he reports getting voltage at the load.
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Your Ride: 1998 540I
Voltage on break lights
If you have voltage on the sockets means that there is no ground on that circuit, once the break switch pedal is depress the switch closes the circuit and you should not get any Voltage on the socket. Your problem must be your break light switch. Your problem should be the break pedal switch.