02 626 2.0 auto no start what sends the signal to turn the fuel pump on??

On my Mothers 2002 2.0 626 automatic 97,000 miles the car will start sometimes if you turn the key back and forth fast many times and then you hear the fuel pump humming.It wont start if you dont hear the pump turn on.I just replaced the ignition switch thing that was it but it wasnt.I have replaced the fuel pump relay and the fuses all check out.
What sends the signal on these cars to turn the fuel pump on??? or is it a faulty fuel pump that is on its last days? I looked under the rear seat for a fuel pump access but there wasnt one?Do you have to pull the tank on this year to put a fuel pump in it?If that is what I should do?I cant keep throwing parts at it hoping it works everytime.I thank anyone that can help in advance!

UPDATE from this old post.It was the Fuel pump!