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Well, it certainly looks like the current through the gauge is what controls it. ie low sender resistance = more current during the pulse = high gauge reading. But it is very non-linear. The 2.5V pulse across 556 R is only 4.5 mA while .54 across 33.5 is 16 mA.
I'd be inclined to connect my variable power supply direct to the sender wire (sender disconnected) and see what gauge reading corresponds to what voltage, plot a graph and then you can maybe work out what would drive an op-amp connected instead of the sender.
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