The LMTV 12 volt trailer connector (on the right rear) is the "7 pin round" configuration with pins on the truck, pointing out. I mention this because two of my trailers are 7 pin blade and I also needed to adapt.
Etrailer sells an adapter, the F77R that worked for my needs, a 7 pin round to 7 pin blade, not what you need, but others might.
You need a 4 pin flat adapter, right? Look at their adapter here:
https://www.etrailer.com/Wiring/Tow-Ready/118709.html
I can't guarantee that 4 pin adapter will work for your trailer, but there's a good chance it will if your trailer is "normal" 4 pin.
But that won't get your brakes working. Most (all?) trailer controllers have to be installed where the driver can adjust them, in the cab. Your M-101 has electric brakes? A '101 behind an LMTV might not need brakes
If brakes are needed, check this out:
https://www.etrailer.com/Brake-Controller/Tekonsha/90250.html
The controller is radio operated and there's a remote module installed on the trailer. The 12v pin 7 on the LMTV could be used to power the remote on the trailer.
Another possible option is to re-purpose one of the blackout light wires from the LMTV's PDP (power distribution panel) to the rear 24v trailer connector (12 pin). Use that wire to route the proportional brake voltage from a normal trailer brake controller, in the cab, back to the trailer.