On a Ford Ranger/Explorer Truck, what does a "Fuel Level Dampening Module" do?

There is a connector under the brake master cyl. that runs to the rear and has the sender wiring in it. Should be a yellow/white stripe wire. Unplug the connector, the guage should read empty, ground that wire on the harness side that goes to the dash, and the guage should read full. You may have to cycle the key to get around the slosh module timer.

If it operates properly, the problem is in the harness or sender to the rear. If not, the problem is the guage/slosh module. Which are replaced as a set, by the way, because they are calibrated to work together.

It could, but an open circuit in the wiring or tanks sending unit will cause the guage to go past full and stay there. Not many slosh modules go bad, I would check your wiring to the tank..

Keeps the level sensor from reading higher and lower than the actual amount of fuel in the tank, when the fuel is splashing around inside the tank.