Electrical Problem?

Debris in the tank? Not sure how hard that is to check for, though, so...

I'd rule out wiring or electrical looseness or corrosion first.

Looks like the sensor is a simple float mechanism.

I had one in a VW that was erratic - the float was cracked and partly full of gas. Since this isn't jumping around, I'm going to guess bad ground on the sensor, or go with @plplplpl for loose or corroded connectors.

I think odds are better that the hesitation is something else, instead of linked to the gauge problem, but there's plenty of Real Mechanics here that should enjoy this puzzle.