Right rear signal light stays on even with the car keys off?

It sounds like the Rear Electronic Module is out (REM), but we should check the fuses. here are the wiring diagrams and fuse locations with a guide to show you how to check with instructions below to show you how to change the REM out in case you need it.

https://www.2carpros.com/articles/how-to-check-a-car-fuse

It looks like the REM self learns so no programming is necessary. Check out the images (below). Let us know what happens and please upload pictures or videos of the problem.