sounds to me like the wiring may be faulty, the rev counter wire is the same one that triggers the relay to kick in so could be that,

the rich running/revving is a separate issue i would say, but clearly until the relay issue is sorted that cant be checked.

its initial prim is all working fine so has to be that trigger wire, need to measure the resistance really but as a temp measure run a wire from the green at the coil to the relay and that should sort it, assuming the relay works of course