This site says the interim vehicles used in 1982 for stateside training were Chevy Blazers.
https://www.usafpolice.org/glcm-program.html
One of the pics on that page also shows a Peacekeeper. Some definitely did serve at air bases in Germany.
I asked the same questions over on Steel Soldiers, a forum for military truck enthusiasts, and one of them was local to Greenham Commons and had a bunch of pictures.
Chevy Blazers were indeed forward deployed and used until the very end of the GLCM deployments (I've got video from an exercise in 1988 confirming it), *and* I got confirmation that basically all of the unidentified "supply trucks" were M923 five-ton dropside trucks.
At present, my best guess for the tactical organization of the mobile units looks like this:
One flight = two elements.
Each element will have one Launch Control Center (with MAN tractor) and two Transporter Erector Launchers (with MAN tractors); one 5-ton general supply truck (with water buffalo trailer); one 5-ton truck with fuel tanks and a generator trailer; and five security vehicles (Blazers, HMMWVs, or local equivalents).
One of the elements will have another supply truck and a 10-ton MAN wrecker (to unwreck the missile trucks).
Squadron command contains another 10-ton MAN wrecker, at least six security vehicles, and at least six 5-ton trucks, four of which carry large shelters on their beds. All the security vehicles from the picture were hauling trailers, presumably loaded with gear for setting up camp. From footage out of Germany I identified what looked like a 2 ½-ton assigned to a decontamination unit (they were hosing down an LCC that passed by their location while relocating). It *might* have been an older 5-ton though.