relay system - fuel pump

I have a 95 gmc jimmy and all of a sudden I started having a hard time starting it, I took it to my mechanic and he could find nothing wrong but did change the relays anyway. It ran fine for about a week now it's back to starting only once in a while, the mechanic told me to try wiggling the relay alittle and that seems to work once in a while but not always, the times it does not start I don't hear the fuel pump start but after alot of relay wiggling I can finally get the pump to start, does this
sound like a fuel pump problem or something else? Also since the
relay change once in a while the hot air will go cold and the engine will start to run very hot and after a few minutes it will go back to normal,
and a couple of times the headlights will just go off for a few seconds while driving. Sounds like I have major problems doesn't it?