2005 Chevrolet TrailBlazer - Why now?

All of a sudden my key fob, rear wiper, dome light, and radio shuts off when I turn the car off (used to stay on for 10 minutes)

There might be a function that shuts these systems down immediately if the computer detects a low battery. You might start with the condition of your battery, state of charge and a load test.
But why do you want your rear wiper and dome lights on? Yes, occasionally I will be listening to the radio after a turn off my engine, but use the dome light only as needed.

The dome light doesn’t come on when I open the door, both key fob don’t work, the rear wiper doesn’t work, and when I turn the ignition off the radio goes off immediately (it used to stay on until I opened the door)

Most of this is controlled by the BCM which is located in the rear tailgate . Sometimes the wires up at the rear tailgate joint in the rubber boot will break and you will have to fix the wiring . The other thing you can try is to reset the BCM pulling two fuses that feed them . I dont remember if those fuses are under the hood fusebox or the one under the rear seat .

What is BCM?

https://moduleexperts.com/5-common-symptoms-failing-body-control-module-bcm/?gclid=EAIaIQobChMIzejg0_2g4gIVCavsCh3uYwr5EAAYASAAEgLeIPD_BwE

Tester

BCM= Body Control Module or the computer that controls those functions.

Thank you for explaining

Have you ever changed the key fob batteries? The truck is 14 years old, and the batteries do wear out. Check the dome bulb to make sure it isn’t just burned out.

Retained Accessory Power (RAP) function can be defeated due to low battery power or if the BCM thinks any door is open. Since the rear wiper is affected, it could be bad wiring in the rear hatch, usually where it runs between the door and body.

I’d check fuses first. Then wiring. Then BCM.

Re BCM

Cars used to be configured with dashboard switches that were directly wired to the light bulbs, radio, wiper motor etc directly. Now-a-days the switches often connect to a computer (the body control module), and the computer is what turns on the light bulb, radio, wiper motor. The advantage of this modern configuration is it reduces the complexity of the wiring harness. A single wire can communicate the turn on, turn off commands using digital pulses addressed to an assortment of devices who monitor the signals on that wire. It also makes it possible to have special effects, such as lights that dim slowly to off, or stay on for 10 minutes after the car is turned off, then go out, etc

First thing I did, thanx