Small Engines (Lawn Mowers, etc.): Riding mower problem, engine manuals, kohler engine

Question
I have an older Gravely 18H riding mower with a Kohler engine. It starts fine and runs for about 2-3 minutes and then stops dead. After that happens, when you turn the key nothing happens, no click, nothing.  If you wait 10-15 minutes and turn the key, it starts fine and runs for another 2-3 minutes and dies again. Because nothing happens when you turn the key after it has died, I'm guessing this is an electrical, not a fuel problem. Battery is fully charged, spark plugs are newer and not fouled. It seems to me like something is overheating and shutting off a relay that opens back up when it cools down againg. What comes to mind is the ignition coil, does it sound to you like this might be the problem?

Thanks!

Answer
Can you send me the mower model and serial number?  This link describes how to find your mower model and serial number:

http://apache.ariens.com/cgibin/ctrg0005?SESSIONID=142212940&site=gravelys

The engine will have it's own model and serial number.  I need these numbers as well to look up the engine manual.

It could be a the coil but I need to look at the mower and engine manuals to see what electrical components you have.

Eric