my 88 305 tbi will start right up but only runs a few seconds. If I keep pumping the gas it will stay running but really rough. Also,by doing this after a few minutes the whole exhaust system gets really really hot. I looked at the two injectors while someone keep pumping the gas and it looked like they had a good spray pattern. Then I had them start it without pumping the gas. It ran for 2 or 3 seconds and died. In this scenario at idle the injectors had no spray pattern at all but there was a little fuel coming out the injectors. Now, Should I have a nice spray pattern even at idle also?

i had the same thing that happened, i put so much time and money int my 91 and found out it was just the fuel pump. good luck

If it is a bad fuel pump that still don't explain why the exhaust is getting so hot.

I had the same problem. But the car ran longer, by maybe 5 seconds, with the map sensor vacuum line unpluged. With it plugged in, it died immediatly. Check fuel pressure. My spray from the injectors looked a little weird at idle, with the throttle open it would run a little longer before stalling. I finally checked the fuel pressure it had like 2-4 psi. Thats not nearly enough to keep it running. Plus my fuel filter was old and had lots of contaminant, that didn't help. The spec for stock tbi 305 is 13-15 psi. You should deffenitly check you pressure. The car would only run for 15 seconds top. Changed the fuel pump, cost me $50 at auto zone, runs great. Good luck!

i would say the exhaust is getting so hot becaus eof the unburnt fuel igniting in the pipes causing them to get hot.

yeah, idk man that sucks. a word of advice is that it is a good idea to do the fuel pump because mine is a 91 and the little hose in the tank got rotted horribly and you should do it as a precautionary step. its best to pull the trim and carpet up in the hatch well and cut a hole in the hump behind the seat. thats wat i did and it was alooottt easier than pullin the rear end, suspension and exhaust. good luck