Fuel pump not working at startup of 1985 Camaro

Fuel pump on 1985 Camaro
I'm experiencing problems starting my 1985 Camaro. (It's a 2.8 Liter fuel injected V6 with five speed standard transmission.)
When the car has not been used for an hour or more, it requires cranking the engine three or four times before it will start. (It never took more than a second to start up until about a month ago.) I have determined that the fuel pump is not receiving power when the key is first turned on. But the fuel pump runs fine once the engine is running.
If the car is started within an hour of the last time it was running, there is no problem starting the engine at the first crank. When it has taken more than one crank to get started, the check engine light stays lit for as long as the car is running. (I don't have any means to check the computer readout.)
It seems that for up to an hour after shutting down, the system maintains enough fuel pressure for the engine to start, even with the fuel pump not running. And once the engine is running, the fuel pump starts and continues to run fine. The fuel pump does start up if is jumpered directly to the battery.
Can anyone suggest what might prevent the fuel pump from starting up when the ignition is first turned on? Apparently the pump only starts when oil pressure is high enough, either from cranking the engine or as the engine runs.)
Regards, Bill
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