Holy back from the dead post Batman!
There is a case to be made about just replacing a bad inertia switch but there is also one to be made about eliminating it. I have had issues with them before, one was faulty and left me stuck. The other every hard bump or pothole (and anyone from PA knows there are plenty of potholes) would cut it out for a split second. When it gives me trouble, I deal with it, either try a replacement or eliminate. The ignition shuts off the pump too.
IIRC, the wiring for the inertia switch goes to the relay so it’s not full power to the pump as has been suggested. If you are going to splice it, a jumper can be used for temporary testing but I wouldn’t make it a permanent fix. Don’t mummy it in electrical tape or use a household wire nut either. Solder and heat shrink is preferred or one of the solder-shrink connectors that you heat and it does both steps at once. Wiring a separate switch inline to use for anti-theft works too and a standard auto switch is fine.