Here's a simpler circuit which amplifies a sine input from a sensor at terminals 1,2. The output at S,V, is a similar shape with a peak-to-peak voltage clamped at 12V (the assumed supply voltage). Note that the voltage difference between S and V has both negative and positive peaks. The polarity of both capacitors needs to be correct.
This circuit will not work as hoped if the TCU checks for a DC sensor resistance, but may work if it is looking for an input which goes above and below S.
A sensor signal of 10Hz or more and an amplitude of 0.5V or more is enough to raise the output to clipping level.

This circuit will not work as hoped if the TCU checks for a DC sensor resistance, but may work if it is looking for an input which goes above and below S.
A sensor signal of 10Hz or more and an amplitude of 0.5V or more is enough to raise the output to clipping level.