What was the age of the car that you tried the replacement gauge from? as the wiring an eletronics changed overtime (with the introduction of the facelift). The fuel gauge is not a simple analogue controller, the signal from the sender is a PWM digital signal which is then converted by a small chip in the gauge to value displayed.
However it is not as simple as that, it is the gauge that smooths out the fluctuations of the readings (as the car goes up/down hill/round corners) therefore it does perform quite a few smoothing calculations.
The behaviour you're seeing is the controller starting up (and I presume waiting for a valid signal) and then the 15 seconds at the end is the controller shutting down (the gauge has a "always on" live feed too - mainly for the clock).
Have you tried taking apart you guage and eyeballing the circuit?
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