Have you checked for skimmer internal leaks? If the skimmer does not hold water level steady enough the internal water level in the skimmer will fluctuate.
Could it be that something is leaking? valve, water passing out of the skimmer through the fitting, cracked chamber, loose plastic screws?
Anything intermittently blocking the water output from skimmer?
Other then that check the amps of the pump with
clamp on Amp meter when it changes the level to see if Amp reading will fluctuate when water level changes.
See if there is any blockage or debris in the pump volute or impeller body or shaft.
You may be right though to suspect the pump. Because they do have internal "SMART" circuit that is not so smart.