Nick
According to the 410 wiring diagram, a copy of which may be found on this forum if you search for "410 Alternator charging fault" (I put it there under my then nom de plume PEU186F) there is a white cable feeding power from the ignition switch to the rev counter. There is then another feed from this connection to the petrol reserve switch. There is another white cable which is looped through a link on the back of the rev counter which feeds power from the ignition switch to the ballast resistor and thence to the coil and the distributor.
I imagine your car will be very similar, Bristols weren’t renowned for changing things for the sake of it
The rev counter works by interpolating the rate that the distributor points are opening and deriving the revs from that. Rev counters accordingly came in 4, 6 and 8 cylinder variants.
Your Rev counter could have failed because of an earthing fault, but we can rule that one out as the warning lights share the same earth via the distributor housing
It could also have failed because no power is getting to it. But I note that the feed to the petrol reserve switch and its warning light comes off the same connection point on the back of the Rev counter, so if those work that rules that one out.
It could also just possibly have failed because the feed to the distributor that is looped through the link has fallen off - this link can be undone and opened - but I think that really rather unlikely.
The most likely explanation is that old age has caught up with it and it’s given up.
In all events you’ll need to get at the back of it, which involves disconnecting the battery, removing the steering wheel, removing the instrument cowl and very probably loosening the instrument panel to get at the back of that in order to get it out.
If you do need to get it repaired may I suggest JDO instruments who may be found via the following link
Home page
I found them (actually I think a one man band) excellent.
Good luck - by the way it is a mistake to assume that it retained any accuracy over the years, even if it is a piece of electronic kit. By now it could easily be out by +/- 40% - I speak from experience, but JDO will recalibrate it for you.