So unfortunately no improvement after rewiring to fuse 12 so I think I will need to go the diode route as per next suggestion - I like these little challenges gets the brain going a bit
Try swapping the signal line from 3 to 4. Have you got contact breakers? If that fails, try sticking a diode (1N4007 will do) in series with the line from the breakers, with the cathode (stripey end) towards the tach. If these are like the VDO tachs, they don't (oddly) like voltage spikes pulling the the signal line below 0V. The diode should fix that.
...although it is odd that it played up previously with the headlights on . I'd also check the rest of your wiring.
Sort of If there was a total brain fart going.on , I would reckon its being powered off either the backlight supply, or badly from the coil signal, with 12 volts being totally missing on the power lead, or the ground is missing.
Half an hour with my Fluke scopemeter and I could tell you exactly what the problem is.. The IN4007 diode is one good idea, then the next level would be e.g a 2k2 resistor from coil negative to the striped end of a 12 volt zener diode, other end of zener to earth. Feed tacho from junction of resistor and diode. Converts signal to a 12 volt feed, stops ignition coil noise going all round your wiring.
Just another odd thought: you have got it set to 4-cylinder operation, and not being driven by an alternator ("W").
Just found the instructions in the depths of my van and saw that they suggest a shielded wire so I think you are correct in your diagnosis