2002 jaguarxj8 when brakes applied, computor message ; check rear ligh ts ; all bulbs ok.connecter plugs taken off and on.

The brake light switch is on top of brake pedal arm. Check your bulbs, and connections to the rear lights (unplug harnesses and clean the connectors as well as bulb(s) etc... )

Also, it (shouldn't) be the brake light switch if you can shift out of park. Good luck.

the third light works off the light cluster main wire at the rear so if there is power to the this light then there is a problem with the cluster link. check with a meter at the connector with the brake applied if power. then clean the plug to the cluster.

check the type of bulb in the left turn signals. sounds like the wrong bulb has been installed

The entire brake light system has, at best, one fuse. In fact, the fuse that the brake light current flows through probably feeds more than just the brake lights.

If the same filament is used for brake light and turn signal, the power to the brake lights goes through the turn signal switch. When turning, the brake light power is disconnected from that light by the TS switch, and the flasher is connected to that light instead. So a bad TS Switch can fail to reconnect the brake light power to that light.

If there is a separate light or lens for the TS and the brake light, that doesn't apply.

brake lights not operating may be the brake light switch located screwed into the pedals box just below where pedals pivot it has 2 wire plug attached unplug this plug then using either a short wire or a matal paper clip opened to form U shape connect the 2 wiresin plug this should put b/lights on with ignition on ?provided all bulbs are ok ?? if it works then ? check the switch it has a plunger on it and when pedal pressed it moves out to put lights on however being plastic ? the plunger may be stuck use wd40 or similar and lubericate and work piston so it pushes in and springs out freely ? then refit wiresplug and recheck lights work ok ? also check on brake fluid level in reservoir top up and ensure no leaks when brakes applied ?

Check for blown fuse on that circuit,
Check ground connection is ok/intact at the rear light bulb sockets.

if u checked all the fuse's both in the cab and under hood and the wiring harness at rear of truck for any damage, I suspect the turn signal switch is defective.

sounds like brake shift interlock is not sensing brake pedal apply so it can activate solenoid to allow shft from park.
Check bulb socket and replace if bulb ok

take the bulb back out have someone sit in car apply brake get your self a circuit tester and check to see if this circuit is carrying efficient 12 volt current! some times in cold weather these bulbs get hot with long period of breaking and when released condensate and rust begins and you get what you have perhaps bad socket! this would be a ideal location to begin and probably end,

did you check the bulbs , etc. ? Do your turn signals work ? Check for corrosion on the bulb contacts or connection.