The dome lights will not turn off, why?

Probably the door jamb switch has failed available at your local auto parts stores

Does your light go out when you push the switch button in.If it does a quick fix is go buy a pencil eraser and slide on switch.It works.

Be aware that the switch can be lengthened or shortened. It is pressure fit into its metal collar, and can slide in that collar under pressure. In the case of my '93 Ford RV (van) the switch had slid, for some reason, and the previous owner had put a wood shim atop the switch and duct taped it to try and compensate. It was a crappy solution, which meant the dome light sometimes didn't turn off, explaining the battery drain problem I was having. With a long socket and a rubber hammer, I was able to lightly tap on the collar to slide it down the switch and make it longer than it should be. I re-installed the switch and closed the door on it; the closing door forced the switch to slide to its proper length. Note: I hadn't known it, but (1) my dome light is on a 25-second timer, and (2) that timer doesn't start if the door is open less than a second or two. Not knowing this caused me some confusion during troubleshooting.