Hello all !
I finally made some progress on this issue

Here’s the little test rig I set to calibrate the tach and the final result:
I used a 3€ square wave generator, a salvaged 12v power supply and a USB oscilloscope I bought many years ago...
Funny to observe that the response of the tach is not perfectly linear, when 1000 and 6000rpm are aligned, 2, 3, 4 and 5000rpm aren’t....