I dont believe the 05 radio is controlled by CAN. For the sake of not attaching a dozen pics I posted up the Smart Junction Box (SJB) on another thread recently. It will show what connectors go where and what each fuse goes to. It's not a fuse issue otherwise you wouldn't have power come and go. If anything, possibly a relay if it's in the SJB. They are known to do some odd things...
https://www.expeditionforum.com/threads/diagram-search-help.40667/
Attached you'll see pinouts for the plugs at the radio and the last one is ignition in the steering column if there is in fact s problem w accessory. You could then check it there to see if it voltage stays or goes on that circuit to see if something is related to the ignition switch.
I would take the radio out, have someone ride with you supporting it and watch to see if voltage changes while it does this come and go type thing so you can see what happens when it's working and when it stops. As long as the key is on or vehicle is running you should see 12v at that wire. Anything else would indicate a problem and at least narrow it down a bit.
You'll only need basic tools to remove the radio. There are two fasteners in the top of the bezel above your instrument cluster. The rest if it just pops off carefully. Start from the radio side, tends to be easier. You'll want a plastic tool to help pry. A screwdriver will scratch the finish of your dash or break something...or both. Lower the steering wheel all the way and just work the bezel toward you and out. It requires a bit of force, a little bending, and dont get frustrated. If you yank on it it will probably snap. It's not a cheap part unless you can find at a you pull it yard. YouTube for a preview if you have no experience removing interior trim.