You seem to be stuck on the fuel pump; however, we both know a coolant change in the radiator and coolant reservoir is long overdue. That's because coolant doesn't change itself. Once that's done, the fuel cap assembly can be removed, the fuel pump's wiring checked for flaws, the pump's terminal connections can be checked for tightness and the pump's sound can be analyzed for changes while the engine is running.
You could do a check of the throttle switch to be sure it's set correctly. If it is set correctly, try to get in the habit of closing the throttle completely when decelerating to lessen backfire, but only one pop per engine brake event isn't really a big deal, unless it's rattling windows in the neighborhood.