94 E34 525i transmission problem

my 94 bmw 525i has some issues with the transmission. There are a few things that seems to be connected. First off; ithe dash reads that the brake light is out but all light are working. With the headlight
'OFF' and the transmission in reverse..... the dash lights goes dim. With the headlight 'ON'... it does not get dim {it works perfect}.
PLUS.......... the transmission works well in normal driving but when the pedal is pressed to the floor [kickdown] the engine just revvvvvvv out without the transmission shift. So there is no downshift. Also there is a slight longer than normal engagement of the reverse gear.
To sum this up: 1. brake light warning.. but all lights are working. 2. dashlights goes dim when in reverse and light are off. 3. tranny work well until pedal is pressed to downshift point.. just engine rev out. 4. delayed engagement of reverse gear. I think its electrical problem somewhere in the system... any help would be appreciated..
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Wiring / ECU fault - has it got tow bar electrics? This one is common and on older models the light won't go off after starting until AFTER the brake pedal is pressed.

You have an electrical fault. Normally the dash dims when the headlights are switched on.
Either there is a big fault with a short through the reversing lights or a little fault with the reversing light switch also asserting "headlights on" to the dash ECU.

Kick down switch not working? Or it could be very strong spring. I used to have a 740i with a 5 speed box. Normally it would downshift if you pressed hard on the accelerator, but usually not above ??mph. One day I had some sort of emergency and really floored the accelerator and hey presto actual kickdown.

Normal - more bands etc. to disengage and part of the box has to stop (enter neutral) and change direction.

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