Left mine on overnight one time, had to jump it in the morning, it started fine. The Jeep died 8 or 9 times in 8 miles. finaly 1/2 mile from home it would'nt start at all. Swapped it out for a known good (module) used one. That was a 1000 miles ago. Sounds to me like you've found your problem.
on edit. had no goo but looked like there was lots of heat.
1957 WILLYS pickup, needs work.
1973 J 4000,
1978 CJ7 DD.
1979 CJ7 360, TH400/Quadratrac trail Jeep.
1980 CJ5 trail Jeep.
1983 CJ7 pretty weekend and sometimes to work Driver in the summer, My first rebuild, if the Q-trac and 5 are broke, this one is the one to take. its just as capable as the other 2, except nice paint.
1984 Grand Wagoneer, 1 ton axles, great 360/727, and a big a$& tree fell on it .
1989 YJ the CJ to YJ conversion.
2005 TJ Rubicon.
2011 Grand Cherokee Laredo 4x4, Mrs. LUCDOG's DD.
Lots of parts not for sale, i'm a hoarder.