Replaced fuel pump motor on fuel pump assy, have voltage to each of two wiring connectors, but no pump action and fuel gauge is inop

I have to ask. How long since a tune-up? Are there any applicable trouble codes?
With engine cranking, if no spark at the spark plugs and no fuel injector pulse along with no fuel pump action, have to check rpm signal.
If you have spark and fuel injector pulse but, no fuel pump action, then we check the fuel pump circuit. Did you check applicable fuse, not only check the fuse, check the fuse circuit for voltage. At the fuel pump connector, gray wire is voltage for fuel pump motor and black wire is ground.

their are 7 recalls on the 07 none are for an electrical problem with lighting system
http://www.pontiacproblems.com/recalls/G5/2007 and the following tsb from march 2010 is for flickering lights

• TSB #PIC-5073B NHTSA ID #10034409
  • Date Announced: MARCH 01 2010
  • Additional Info: How to Fix
  Summary: CHEVROLET/PONTIAC: VARIOUS ELECTRICAL CONCERNS. SIR LIGHT, IP LIGHTS FLICKER/INOPERATIVE, PARKING LAMPS FLICKER/INOPERATIVE, TAIL LAMP DIM/INOPERATIVE, TRUNK OPEN LIGHT, RADIO INOPERATIVE DOOR LOCK INOPERATIVE, NO START, NO CRANK. POSSIB
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ELECTRICAL SYSTEM:WIRING

• TSB #PI-0817 NHTSA ID #10047261
  • Date Announced: SEPTEMBER 01 2012
  • Additional Info: How to Fix
  Summary: CHEVROLET/PONTIAC/SATURN: ENGINE FAILS TO START AFTER ENGINE CRANKS DUE TO FUEL PUMP WIRE HARNESS CONNECTOR NEEDS REPLACING, WITHOUT REPLACING FUEL PUMP COVER ASSEMBLY (FUEL PUMP FLANGE). MODEL 2007-2010 COBALT, G5, ION. *PE
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ELECTRICAL SYSTEM:FUSES AND CIRCUIT BREAKERS

• TSB #PIC-4578 NHTSA ID #10022806
  • Date Announced: JUNE 01 2011
  • Additional Info: How to Fix
  Summary: EPS/STR WHEEL CONTROL FUSE (#19) OPEN. *KB UPDATED 10/04/07. *NJ UPDATED 8/7/09. *PE UPDATED 8/1/11. *PE
  
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• TSB #PIC3385 NHTSA ID #10020916
  • Date Announced: FEBRUARY 01 2008
  • Additional Info: How to Fix
  Summary: REPEATED PARK LPS FUSE OPEN. *KB (ADDITIONAL INFORMATION) UPDATED 4/1/08. *NJ
  

2007 Pontiac G5 Recalls CarComplaints com

Make sure the battery has a full charge.

Are you missing anything besides fuel? Engine cranking visually check for spark at the spark plugs. Also, check for fuel injector pulse. If your missing everything, check for an rpm signal.

With the spider fuel system, start-up fuel pressure can be critical, around 60--66 psi. At the fuel pump connector, engine cranking, gray wire is voltage, black is ground. If good voltage and ground with no fuel pump action, have to suspect the fuel pump.

Four wires the the sender unit. One will have 12 volts all the time with key on. This is the fuel gauge. One will have power for 2 seconds when the key is turned on. This is the fuel pump. Two of them will have a constant ground. Grounds will be black, black with a colored stripe on it, or have a black stripe. Check the harness plug plug for voltage, again it only last for 2 seconds. If you have voltage at the wire. replace the pump. If not, probe the wire about 3 inches back from the plug, check for voltage again. If you have voltage there repair or replace the plug. Most wires break right behind the harness plug.

the two thick wires are for the pump and the other two for the fuel gauge ,check for voltage at the pump if no voltage then follow the wires back to see if their is a connection somewhere ,also check the earth connection if no power in the two wires ,ie one probe onto the earth and the other to a suitable ground on the bodywork ,then continuety

You should only have one power wire on the pump and one should be a ground are you sure you have power on both?

Would you not be better off just checking
fuel pressure at the motor with a gauge,since
for some reason the pump runs when you tap
on the fuel tank

You sort of answered your own question

check wire to fuel pump assy in tank. Likely corroded connector there or a bad sending unit in tank.

It sounds like a problem with the fuel gauge sender unit in the fuel tank which has worn out and gone open circuit and needs replacing. Access to the unit is usually through a removable plate in the floor in the rear of the vehicle. Disconnect the wiring connector and any hoses and then remove the securing screws. Replacement is done by reversing procedure.