Reverse comes on when brake

check for a bad ground in the tail lights harness
if you have a light control module check/ replace it

It changes down a gear because you applied the brakes. Check the rear brake lights for a blown bulb.

The reverse clutch is probably worn out. Transmission needs to be rebuilt.

Check the fuse box before you change anything, after that call a dealer or auto electrician/ knowledgeable neighbour.. Do you have a repair manual? Is there any reason the wiring harness has been hit, check the boot and bonnet connections, brake lights and reverse come through the side of the boot area. Has something pulled the harness?

it could be a ground problems .. if ground at brake lights is not good then it could take it through back up lights
check all ground to rear end like parking lights,brake lights, back up lights and flasher
if you have a trailer harness check connections for trailer could be a big problem
hope it helps

Have the catalytic converter checked at your local muffler shop...clogged...worn out...Hope this helps.

you must have your wires cross ,have another person press on the brakes .and put car in reverse to determine which wire is which, remember that the reverse goes on the clear part of fixture

Sounds like someone put the bulbs back in the wrong holes in the taillight. Or two wires are shorting together. Either way , I think if you remove the taillights , you will find the problem easily.

Sounds like some crossed wiring or perhaps the connectors to the lights are swapped if they are the same connector. I would start with the brake lights and make sure everything is hooked up the way its supposed to.

check the wire harness that runs from inside the trunk on the drivers side follow it down to the tail light and make shure the wires are not damaged or unplugged remove cover on the drivers side inspect the bulbs the holders and the wires and dont forgt to retighten all grounds that you find on your travels this should get the rear tail lights working also check the brake pedal switch up on the metal part of the brake pedal arm follow it up tp the brake pedal switch and acuate the switch by hand and check the wire voltage coming in and going out when pressing the brake pedal ok give this a shot