You can certainly create a product that does not require any external power to do this job. But far more information is needed than you're giving.
Is the tach output differential floating or referenced to chassis ground? You've already told us it's a 10V amplitude. Is that unipolar?
What does the speedometer require in terms of signal amplitude and pulse width? Many require a minimum pulse width of several milliseconds, and few to many volts of amplitude for noise immunity. Back in the day, signal amplitude was the main fallback to achieving noise margin.
What range of RPM are you dealing with? 0-RPM?
With that out of the way, you need to concoct a /static/ logic circuit to process and transform all the signaling. And that means no timing components. As for internal power, a coin cell form factor with an exceptional shelf-life will make the circuit, in effect, a forever thing.
Something like this, with a 20-year shelf life.:
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You can use 2x CD4018B's for the logic, and /maybe/ a dual N-channel MOSFET for an analog pass-through switch; it depends on info you haven't provided. Both of those have very low equivalent power dissipation capacitance, 63pF for CD4018B due to the Johnson counter topology, 150pF for FET input capacitance. As in this, which even DigiKey sells on the cheap:
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May need or may not need a protective TVS and some transient filter caps. You do need some decoupling for the logic, which is minor. And you need some creativity in your circuit design, especially with the choice of COM for the battery; it depends on info you haven't provided.