O.k., A quick search on the 'net showed that it WAS a front deck mower. Grasshopper with different paint on it. Although I work for a Grasshopper dealer, about all Grasshopper tech. support will admit is that they made the mower. All service is supposed to go through a Woods dealer.
I recall working on a similar grasshopper once that had all kinds of start/run issues. Had a Briggs & Stratton Vanguard on it. lots of cut/ spliced/ jumped wires on that one too. After becoming totally frustrated finding and fixing different 'upgrades', what we eventually did was replace the complete wiring harness with a new one. It fixed all the start/run issues.
You can, (if you are patient and persistent enough) obtain a wiring schematic from Woods. Trace every wire on there and verify that it goes where it is supposed to go and nowhere that it is not supposed to connect. This should correct all your wiring problems, provided you have the correct ignition switch and with the possible exception that there are usually two diodes on the circuit board in those mowers, one of them could be bad and sending 12v to your coil.