Small Engines (Lawn Mowers, etc.): 30 plus year old Gravely tractor, wt oil, air hole

Question
I have a rear cast iron mounted engine;that was rebuilt 6 years ago.It was running bad and would backfire when turned off. put new plug,new air-cleaner;and replaced melted connector with longer wires (2)-they come out of engine ;below carb.;. And I added about a cup of #30 Wt. oil;Iforgot I had sythetic oil in it.Anyway it starts great ,runs for about 5-10 seconds and dies-out.  ENGINE:K301S   SPEC.# 47614d   MANUFACTURER : KOHLER CO. THANKS  TOM

Answer
Thomas
check the little air hole on top of the gas cap, if it's clogged,no air is getting into the gas tank to help move the gas around. I know it sounds simple but that was the reason a lot of mowers wouldn't stay running. If it's clogged, clean it out by tapping hard on it or use a thin needle to clean it out. If you can't get it cleared, purchase a new one. Also check the fuel filter, that could be blocked as well.

When this mower dies have you checked for the usual things like spark? Does this mower have a primer bulb? If so, can you push the primer bulb and the mower recover for a moment or so? No spark could be a heat related issue with the Coil. The gas cap issue I have experienced on an older Briggs 5 horse. If the vent for the cap is plugged, it will keep fuel from flowing properly and it could take up to 10 minutes of running for the issue to edify itself