I would investigate the evaporative control system on Wendy’s Yukon which makes sounds like someone is beating on a 55 gallon drum shortly after she walks away from the truck.
Thinking a vacuum is being drawn on the gas tank when the truck is running. Then the release of vacuum lets the tank pop back out.
Would also contribute to the 2 MPG problem.
I also think the 2 mpg problem could be the key. Could unburnt fuel be getting into the catalytic convertor, or anywhere in the exhaust system and igniting once the engine is switched off? It might do it more when the car was cold as it would be running richer so more gas would be being pumped in.
I think it might be her oil pan flexing when the oil flows back into the pan. I bet it makes a similar noise, at a higher pitch, just after starting, but isn’t noticeable from within the car. The noise she is hearing would be louder on a short drive because everything is still relatively cold and hasn’t expanded. Expansion would reduce the noise. There are 3 large faces of metal on the oil pan and each would have a different sound. The sound wound be a deeper tone because of the amount of oil in the pan. The oil doesn’t flow back into the pan the same way every time so it makes a different rhythm each time she stops.
-Mike