Richard. You have now several posts where you talk about 10-700Hz as input frequency. It isn't. It's the intended output frequency.

Anyway - unless there are extreme needs (which does not seem to be the case), the problem can be solved quite easily in a large number of ways in software. Both based on the input signal as digital pulses and the input signal as a sine wave with ability to pick up phase of signal using an 8-bit ADC input.

A software-based solution can have all parameters modified almost instantly. A hardware-based solution requires changes to component values.

In the end, it's just a question of how fast the output frequency should change for a change of the input frequency, and how exact it should match a 10-times frequency increase. And if an integration over say 10 minutes should show exactly 10 times the number of pulses, requiring the algorithm to keep an error component accumulating the difference between nominal and actual behaviour and trying to zero that error component.

If the design allows a 1 second delay between input and output, the problem suddenly became trivial. Count number of pulses during second n. Emit 10 times as many pulses during second n+1. Almost no code at all involved. With a sine wave input to an ADC, very trivial code can manage almost perfect behaviour with maybe 0.2-0.3 second response lag. The lag mainly caused by a need for a low-pass filtering of the input to make sure noise on the signal don't fool the system into making a huge jump in output frequency.

By the way - a diesel engine can change RPM quite fast. It's more a question of what kind of diesel engine. It makes a big difference if it's an engine for a truck or for a premium car.

"yet I don't see the 10x multiplier"

But you don't agree with the information in the original post? That the sensor produces a frequency that is 0.1 times the frequency the RPM meter expects? For such a condition, there are basically just three options. Frequency-scale the signal. Get a different tachometer. Or get a different RPM meter. Keeping tachometer and RPM display, that 10x multiplier is very much visible in the signal chain.