The purpose of the relay is to provide a switchable "short cut" path for current to drive the injectors thus avoiding carrying that current under the dash and back again to the injectors. I believe that this prevents inducing noise from the rapid on/off firing of the injectors into the radio circuits and therefore the name.

It is a standard relay and it often fails. I may be mistaken but I believe it is the same relay used for the OD circuit and can be swapped. The relay can be taken apart by prying open the plastic cover. You may see bad soldering on the main current carrying solder points on the PCB, they can be reflowed.

The primary ignition circuits can be eliminated as a culprit if you can see the tach moving slightly during no start cranking, this means ignition pulses are getting to the coil negative terminal. These pulses arrive there via the power stage and are also supplied to the tach.