With sincere thanks to Art for setting me on the right track I have fixed the problem and have achieved 100% functionality.
Here is the full story.
The box actually under the dash does contain the safety interlock electronics for the starter circuit and the belly mower. The electronics are a couple of standard logic gates with unstandard numbers. For the starter there is basically two inputs a netural sensor from the gear selector and start from the ignition switch. The output goes to a driver transistor that that energizes a relay coil that sends 12V to the starter solonoid. The problem is that it is a small relay and subject to deterioration, probably environmental. these contacts deteriorate and consequently provide a high resistance connection. While you get 12V at the starter solonoid there is not enough current to pull to the start position. Hence the click but starter will not turn.
Replacement of the relay is a pain unless you you have experience with electronics and have the proper equipment. Replacement of the board if available will be very pricy. So here is a solution that will cost less then two buks that anyone with minimal farmer ability can do.
1 Get yourself a 12V coil relay that is rated for 5A.
2 Connect a suitable length of wire to each of the coil termanals. I will explain what I mean by suitable length of wire below.
3 Connect a suitable length of wire to ear of the termanils of the normally open contacts of the relay.
4 Pull out the connector to the solonoid from the starter. It is on the rear bottom of the starter. Cut off the connector with about 4 inches of wire.
5 Attach the end of the remaining wherer you just cut off the connector to one of the relay coil leads.
6 Connect the other relay coil lead to a good ground. I used an O terminal that I frimpted on a length of wire and connected under a screw that holds the radiator shrod on.
7 Connect the connector and wire you cut off to one of the Normally open contact leads on the relay. Once connected, plug it back into the socket at the back of the starter. At this point you should consider where you will mount the relay. This will determine the length of wire.
8 Connect the other relay normally open contact to the battery. This can be done by running the wire directly to the battery + terminal or to the power input terminal on the starter. If you follow the second option I recommend you use a large O terminal.
That it it. You have just removed the load off the relay in the safety interlock module, maintained the safety function, avoided the high cost of replacement and achieved 100% functionality.
