And if that doesn't work, there's a possibility that an electrolytic cap has failed on the tacho's PCB.
Big Red The 1985 240 had a dead tacho because of this. See Cleanflametrap's pages and article on Turbobricks about replacing these caps.
A third possibility is a damaged PCB track on the cluster's circuit board - this has been known to happen when there's been a short circuit to ground, and the foil track on the circuit board acts like a fusible link.