Check Engine Light on, code P0497?

Very common mistake. No diagnostic fault code ever says to replace a part or that one is bad. They only indicate the circuit or system that needs further diagnosis.

DTC P0497: EVAP System Low Purge Flow

As you can see, the valve isn't even mentioned in this definition. When a sensor or other part is referenced in a fault code, it is actually the cause of that code about half of the time. First we have to rule out wiring and connector terminal problems, and mechanical problems associated with that part.

In this case a good suspect is the rubber hose coming from the charcoal canister. If it is plugged or kinked, it can set this code. While not real common, there have been some instances of the charcoal beads leaving the canister and getting sucked into the hose. Often you'll see those beads fall out of the valve when it is removed.

You're making this somewhat confusing. This started with the fuel gauge not reading correctly, (often a simple fix). Can I assume at this point the Check Engine light and Fuel Cap light have not turned on yet? This is the first mention of the Gas Cap light.

Did those two lights turn on for the first time after the fuel pump assembly was replaced? If so, logic would suggest the pump is not sealed properly. That would have the same effect as leaving the gas cap loose, and could turn on the Gas Cap light.

Again, if the Check Engine light only turned on after the fuel pump was replaced, that might be related to the pump not being sealed properly. There's no way to measure air flow being drawn in and burned from the charcoal canister. Instead, the Engine Computer knows when it commands the purge valve to open, gas fumes should be drawn in to be burned, and that should show up as a change in the readings from the oxygen sensor, which the computer expects to see. With a leak from a leaking fuel pump housing seal, fresh air might find its way to the engine instead. Everything else could be working properly, but the computer isn't seeing the change in oxygen sensor readings it expects, so it assumes too little air is flowing in from the charcoal canister, and sets code 497.

What's puzzling is there should be some other fault codes set for this problem. One in particular would be "small leak detected" or "gross leak detected". Either of those will set when there's a leak in the fuel system including a loose fuel cap and including a leak at the fuel pump housing. Very often when one fault code is set, it prevents certain other tests from running, so other codes will not set, at least at that time.

The place to start is by having your mechanic recheck his work related to the fuel pump. It's not uncommon to miss a piece of dirt or debris that gets caught under the seal. There's other hoses there too that could become dry-rotted and leak, or a hose clamp could rust off.

The purge function only occurs at certain times while you're driving. That can explain why a warning light might turn off at times. For some defects and their fault codes, the lights turn off every time you restart the engine, then don't turn on again until that defect occurs again. That can be minutes, hours, or days later, but the diagnostic fault codes remain in memory until they're erased.

Start with rechecking the fuel pump housing seal, then let me know what they find.