the first thing Id check is the oil pressure is reaching and maintaining at over about 10 psi with a separate gauge, the fuel pressure cuts off if the oil pressure drops below about 5-6 psi (yeah I know it says 4 psi BUT that's in an ideal world, in some cases it takes up to 9 psi with a sticky switch)
remember this part
"When you start an L-98 engine Corvette, a series of events take place that causes the engine to run. Knowing the sequence will help you troubleshoot no start conditions.
Fuel Rail Pressurization:
When you first turn the key to the “on” position, the fuel pump will run for 2 seconds pressurizing the fuel rails. There is a Shraeder valve on the passenger side fuel rail near the rear of the engine and if you measure the pressure there after the pump runs, you should see between 40-42 pounds of pressure. The reading will go to 38-40 pounds nominal once the engine is running.test by attaching a fuel pressure gauge to the fuel rail at the shrader valve, on TPI and LT1 engines its located on the pass side fuel rail
(IF IT WON,T MAINTAIN THE FUEL RAIL PRESSURE FOR SEVERAL MINUTES AFTER THE ENGINE SHUTS OFF,THE FUEL PRESSURE REGULATOR IS SUSPECTED OF BEING DEFECTIVE, OR ONE OR MORE OF THE INJECTORS MAY BE STUCK OPEN
Initial Crank Action:
If you then rotate the key to the start position (assuming the anti-theft system has not disabled the starter), the engine will rotate.
Once the oil pressure has reached 4 PSI, the oil pressure switch will close allowing the fuel pump to run.
(Note that you should have a black oil pressure switch/sender. It is mounted behind the distributor on the driver’s side and if it is not black, it is suspect due to a run of bad units that stayed in the GM parts pipeline for some time). "
btw those oil pressure switchs are a known source of problems, they get deffective, intermittently,at times, they get oil leaks and they just start doing crappy connections at times, ID replace it even if its supposed to be newly replaced, or at a minimum Id get out a V.O.M. and check its opperation durring the start/run procedure, but thats a p.i.t.a. Id replace it and check the connections and wireing.
If thats not the cause Id be looking at the fuel pressure regulator diaphram it may be leaking and need replacing, better still install a adjustable fp regulator, the pump itself may be defective, allowing the fuel to flow in reverse once it stops, you might have a injector thats leaking (constantly stuck open)
this should help also