Same problem for me, only I could not start remotely. I could only stop. My circuit board where the remote switch harness plugged in was a disaster. I wound up using DeOx-it on it and a wire brush on my Dremal tool to get it to work. After it was working I liberally coated the connection Jack and Plug with Dow Corning DC-4 grease and have not had any problems since.
GSMC(SW) U.S. Navy (RETIRED) 1967-10-03 to 1993-11-01
1995 Gulf Stream Scenic Cruiser, Cummins B5.9, Allison MD3060, Toad: 2005 Focus ZXW SES Wagon