I have a 1999 jlg with a ford 2.5 carburatored engine. When I crank the engine it starts but when I release the starter it shuts off immediately. I have good fuel pressure. The fuel pump only runs when starter is cranking I thought it used to run with key on engine off but I'm not 100 percent sure. I'm thinking possibly a faulty engine oil pressure sensor? Maybe it bypasses oil pressure sensor with the starter turning but when starter turning it stops engine too.
I have the very same problem. Did you have any luck solving it?
I believe it ended up being the fuel pump intermittently not working.
Can't say for sure with out s/n, but check power and output at oil pressure switch. When you first crank the engine there's no oil pressure so the carb solenoid gets a signal from starter circuit to start the engine, as soon as engine starts and you release the start switch it drops that power signal. By then the engine has oil pressure, closes oil pressure switch to keep carb solenoid powered up and keeps engine running.