https://www.ford-trucks.com/forums/1...-location.html
Your link would not open for me, but this thread should help, especially Post #3. The 10 mm socket is correct. I had an issue with my Mustang fuel pump one time that unplugging and plugging the connecter at the gas tank solved well enough to get me going again. Might try that with the big connectors on the GEM. And I serviced the connector when I got back to the shop.

 

Here is a pic of a GEM for a 99-03 SD and X, or so claims the vendor. If it's the unit that has the keyless code written on it, I found it on our 04 SD. It's towards the center from the steering column, near the back of the stereo unit, and it's a real PITA to get to. At night you can read the numbers off it (I did) with a good source of light, but in daylight it would be very hard. Getting to it to replace it ... ouch, hurts the skin on my big hands just to think of doing that.

But we found (thanks to that linked thread) that on an earlier SD, it's attached to the under-dash fuse box. We'll check its connections.

 

For some reason on the 99 and 2000 trucks the drivers door switch always has issues. I suppose that's why ford changed it in 2001

 

The GEM is screwed to the back of the fuse box.