Jay, the device you have described is called an "anti-dieseling solenoid" in automotive circles, or an "anti-afterfire solenoid" on Bruce's first diagram. If the combustion chamber is hot enough when you switch off the ignition, some high compression emission-controlled engines can continue to run diesel-style, so just about all automotive engines post-1976 in Australia (a bit earlier in the US) have a solenoid that operates as you have said. If that is what it is, it requires 12 Volts applied whenever you want the engine to start or run, but not when you want it to stop. Bruce's second diagram shows how it would be wired. It also shows the ignition units' kill wire.
The main question to be resolved seems to be connecting the alternator output wires. The generator for the original engine may have been a DC type, with a different kind of regulator connection. This will need to be sorted out.
