I have a 98 xj w/ 4.0 and if I start it and drive say 3 miles or less then turn it off it the starter will not turn over with the key
I have to short the starter silinoid with the key on to start it or wait 20 minutes or longer. If I drive 10 miles no problem. It seam like something needs to bleed off before the ignition can be activated after the last successful start. New battery. I notice that the previous owner also removed the egr and installed a header. This is baffling me.

 

Starter has solenoid built into it ya?

That is problem. replace starter.

Get batt load tested while at it.

Don't rely heavily on starter test at a-zone (cause if its warm when you take it there they will test it, and it will pass cuz its warm.) Just get new one.

combination of new starter and fresh battery should provide you with sure starting/turn-over.

good luck sir!

my 2 cents worth

cpnwrench