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My 01 XJR gives me the yellow light and "Check Rear Lights" daily, but NOT every time I step on the pedal. All of my bulbs are good, have verified with an assistant stepping on the pedal. I figure it has to be a dirty or corroded connection somewhere in one of the brake lights...enough to increase the impedance of the circuit enough to trip the warning light but not enough to prevent the lights from coming on.
You have a history ( from what I understand ) on this model of the brake light lens assembly as a whole has a ground issue
The brake light warnings come on if the current sensor sees low brake light circuit current ( electrical connections or wrong bulb ) or no current ( burnt bulb )
Notice some things involved , your running night tail light ( not brake ) is marked as the blue wire as I colored
Notice the stop ( brake ) light comes out of the security lock control module
The brake switch to command on ground path is dependent on the ignition switch which is dependent on wire / pin 5 to car frame ground which can be disturbed tinkering behind the dash
The starter and alternator need a HEAVY ground strap.
I remember many decades ago when the speedometer on a car would stop working and the cable was found to be MELTED.
Turns out the earth strap would fail and the starter needed to get a ground SOMEWHERE so the speedo cable was it.
Reminds me of years ago when a stiff handbrake was a sign of failed earth straps on LRs. They used the cable as for earth when the straps broke & the heat melted the liner around the cable until it seized up.
I had a similar situation on the Bimmer. I discovered the ground strap was
practically broken in two. Everything returned to normal after a replacement.
