Most likely the solder on the circuit inside is dried out and cracked. Almost like the problem with Bosch fuel pump relays from the 80's and early 90's, except that with Bosch it was a manufacturing problem that they did not care to resolve because it was making them money. Open the tach and use a not-too-hot soldering iron and >electronics< solder (not metal solder) to resolder every connection. It's best to remove the solder if you've got the tool, but be careful not to damage the board. But just heating up the solder and adding a small amount will also fix it (just not for the next 30 years...).

Or also sounds like transistor saturation (for those who care). As transistors get old, they start to leak (current leaks through the "switch" when it is not supposed to). If the leakage is too high, it can cause the next transistor in the circuit to turn on when it's not supposed to, and cause a chain reaction. Diodes can do the same, as well as capacitors. Components also change value with age. If one of the perameters are out of spec, then it will usually first show strange behaviour at extreme temperatures. It will get worse over time. But this takes lots of skill to fix, and is actually not worth anyone's time.

Have fun...