Small Engines (Lawn Mowers, etc.): Starter Switch, starter switch, jackssmallengines

Question
I just replaced the wiring harness and starter switch on my '96 37" Toro hydro walk behind.  Its a rebuild/refinish project after a few years of sitting.  It's a generic switch that's interchangeable with Toro #23-0660 as seen at the top of this web page www.jackssmallengines.com/rep_switches.cfm
When I turn the key to start the engine starts as it should but when I release the key to the run position it quits.  If I manually turn the key to the Off position it continues to run.  The Run and Off positions seem to be switched.  Everything seems to be wired correctly M = Blue wire to engine connector; B = Red wire to Battery; G = Black wire to ground; L = Tan wire to relay and Blu/Wht wire to engine connector; S = Blu/Wht wire to solenoid.  These are the colors I can see at the Starter Switch which match up to the proper terminals. Weather they actually go to the proper places, I'm not sure.  What I listed above is how the schematic shows.
Thanks for any help!
James

Answer
L = Lights
M = Magneto, these days electronic ignition
G = Ground
S = Solenoid/Start
B = Battery

The Magneto and Ground wires sound like they are switched.  I need the five or six digit Toro model number off the sticker on the machine to look up the schematic.

Did you find the Toro model number?
Eric