I have a 2002 mustang GT .My fuel pump is good can connect hot wire and ground and it works but when I connect like it's supposed to at plug in it want work.I have 12 volts at inertia switch on both wires all fuses are good but pump want work when I turn key on Could someone tell me what I need to check

 

If youve got 12v present on the input & output side of the inertia switch,but the fuel pump isnt priming when the key is turned on,and you've already verified the fuel pump itself runs by running jumper wires from a 12v & ground source directly to the pump,that indicates theres likely an issue with one of three things.
1) The wiring between the inertia switch & FPDM
2) FPDM
3) The wiring between the FPDM & the fuel pump

 

Could it be the theft light blinking fast and not letting it come on if so can I reset or do I need to take to shop

 

The disconnection of the fuel pump harness may have triggered the flashing theft light.
Is the steering wheel in the locked position presently with the key off?? If no,turn the steering wheel as far as it will go to the left & right then back to center.Once the wheel locks,regardless of which way you turn it and what position the steering wheel is in once it finally locks,reinsert the key & turn it to start to see if it fires up.If this doesn't work,leave the key in the run position then rotate the wheel both directions to the full stop position & return wheel to the center position,turn the key off,rotate the wheel til it locks then turn the key back to the start position.If the steering wheel trick wont work,switch to your spare key and try to start it (Hopefully youve got another key)

 

Like you said "simple". It's always something stupid with issues like this. did you inspect all the pins and connections at the plug/harness? Voltage flow doesn't lie and like you said, if you can jump the pump and it runs, it's either some sort of safety or controller device. Those years are returnless right? Doesn't the ECU control the fuel pump? ....Just pulled this from LMR to familiarize myself with the 99-04 system.

1999-2004 Mustang fuel pump driver module controls the voltage sent to your electronic fuel pump. Commonly used on returnless fuel systems, the FPDM receives a duty cycle signal from the PCM and results in a variable speed fuel pump operation.

Good luck man. Let us know what it ends up being.