^ You probably have either sticking power saver or accessory delay relay, a bad ignition switch, a bad power saver trigger like a door latch, or the radio itself has a short.
I'd start by swapping the relays with known good ones to see if the measured power draw from the battery through fuse 29 changes (assuming yours also has the drain through #29 as his did), and if nothing changes, measure whether there is 12V on fuse #20 when the ignition off - there should be no power with it off. If there is no power, then I would begin to suspect the radio and unplug it.
If there is power on #20 fuse with ignition off, I'd look at any triggers to the GEM, and if none are triggering (closed circuit?) and the GEM is cycling the accessory relay on after a 45 minute inactivity period (including not opening the doors or reconnecting the battery) then I would start to suspect the GEM itself.
So yeah, there are multiple branches to troubleshoot this, depending on whether that fuse #20 is live when it shouldn't be, when the ignition is off. You can get the wiring diagrams from the link in my sig.
One option here is make friends with a local junkyard and promise them you'll buy "something" if you can try a few parts. Locate same year vehicle, pull the GEM, and the radio (they may have those inside on shelves instead of in the vehicles) and the two relays, and try all these parts while you're parked at the junkyard.
If there's any chance you have a wiring fault, especially if the vehicle has been in a flood or had an aftermarket alarm installed, or rodents chewing on insulation, whatever, then you're on your own to try to guess whether any wiring has been compromised, and use a multimeter to probe for voltage on the affected wires.
Edit: Just noticed that the only vehicle you have listed is a Expedition 2004, so some of the details above may be wrong. If you own an explorer then please list it in your vehicle info. If you do not, you should post your issue in the appropriate forum for a 2004 Expedition.
