Do you drive the Jeep everyday? I ask because if the ignition module was going bad, it would get worse the more you drive. Until it won't run at all.
It does sound like the fuel pump. And like the module, will get worse as time goes by.Have you been under the Jeep, and looked for any wet spots in the metal line from the tank? And where the hoses connect. Remember all the metal and rubber lines are 30 years old, if they have never been replaced.
To rule out a problem with the fuel pickup in the tank, if it were mine. I would secure a 5 gallon gas can, with gas in it, to the area in front of the grill. Run a fuel line from the can to the fuel pump, see if it runs better. You shouldn't even have to drive it. IIRC it sputters at idle.
I assume you've checked everything I posted before.
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.