Idles poorly, but it will run fine when gas is applied. (Theory: Pump)

@emoboyscheming a clogged fuel pump would not supply the larger amount of fuel needed when you rev the engine. It would get worse. This sounds more like an Idle air control valve problem (or failing throttle position sensor) possibly some carbon buildup. Get some throttle cleaner and clean it out. There are plenty of other issues that could be causing it. I would get the OBD scanned to see what codes show up. Not all of them would trigger the check engine light. Let us know what you find out.