W124-Intermittent Fuel Gauge Problem

I have searched past threads to no avail.
Model: 1986 300E

Symptom:
Fuel gauge sometimes reads max full, even when tank is not.
Sometimes it reads accurately. Seems to be no pattern to failure.

Attempts:
Since these symptoms have typically indicated a sending unit failure in the past (other cars), I 'pre-emptively' replaced the sending unit. No improvement. Wires and connectors on tank end are in perfect order.

Questions:
Is this a possible failure mode for the gauge, or is a short in the wiring more likely?
If it is a gauge failure, does anyone have a 'Radio Shack' repair procedure?
I'm good with a soldering iron...

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1986 300E 5-Speed 240k mi.