You are correct that this sounds like a door switch issue. The radio should time out after a couple minutes of not opening the door but if it doesn't shut off then it is not seeing the door open and that is a switch issue.
I attached the info below on how to replace this. Please run through this and let us know if you have other questions. Thanks
Images (Click to enlarge)
Wednesday, July 14th, 2021 AT 6:03 PM