Simon;
If it the original Gen 1 Tach, and it shows signs of life at all (although a generous reading), you can consider yourself quite lucky (most Gen 1s have died a miserable death, and factory recommendation for repair was to replace with Gen 2 unit) ...knowledge about the inner workings of the remote sensing module located in front of the Radiator is scarce, but I expect that the electrolytic capacitors within suffer from the same drying-out issue that the Gen 2 Tachs, with internal circuit also suffer from, with your symptoms as a possible and likely effect.
I'd first try adding and external 10,000uF filter Capacitor on the Tach power line, and reporting any change in the operation.
All else I know and can recommend is on the linked SW-EM page you have visited.
Good Hunting!
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