There is a bit more going on with the IVR. This is how I think it works:
The output is a square wave or sorts with a varying duty cycle. When the senders are all at their lowest ohm values, then the wave from the IVR will have a shorter on time and longer off time. (More current flows which heats up the bi-metal strip faster throwing the switch off faster).

When the senders are at their highest ohm value then the wave from the IVR has longer on time and shorter off time.
(Note the on/off cycle could be reversed as I don't know if the IVR is normally open or normally closed)?

The IVR also compensates for varying input voltages. 12V on battery and 13.8 or so with engine running. Notice that the gauges do not fluctuate as the engine is started or shut off.

The IVR is limiting the voltage AND current by opening and closing.
A common 3 terminal voltage regulator holds voltage constant and allows current to vary up to 1A or so.
So there is a bit different dynamics going on between the IVR compared to a regulator chip.

You would need to look at the waveform with senders at their different full scale values in order to see what is going on. Then an electronic version could be developed.

Also note that the 3 senders (resistance) are in parallel. I know the fuel sender is 10 ohms full and 73 ohms empty but don't know the ranges of the other 2 senders in the circuit. The gauges and the IVR coil have some resistance as well.