That's a pretty normal fault for this set. Dump a few cans of carburetor or injector cleaner in the fuel supply. The L1, (Engine fuel shut off solenoid) and the FL-1 and FL-2, (fuel level switch)and the L2, (Day Tank solenoid) tend to also get gummed up with the lacquer.
I am surprised that you have a MEP-105A! Its the rarest of birds in the Army power generation world. They bought thousands of MEP-006A's and many hundreds of the MEP-115A, (400 hertz) but very few MEP-105A. There simply wasn't enough need for a precise power gen set at the time, other then the 400 hertz generators. I spent almost 30 years working on army gen sets, and saw very few, maybe 10-12 sets. I assume yours has the electronic governor and actuator set up. The OLD, OLD, OLD Hyd governor and actuator were a nightmare to work on. If you look in the -24P you can still find this gear, but we changed over in 1980 I think. I worked more then 8 years on the 115A model. Its the same as the 105A, just a different main gen and a few other parts. GOOD gen set!