Re: 2003 GX345 keyswitch and battery light on
Mike, you said you've had the tractor 6 years. Have you replaced the battery & (if) when? If your battery voltage was only 8 volts, this means: battery is pretty much shot and will not accept a charge, or voltage regulator and/or stator coil not working...as Russ commented.
Although not familiar with the GX345, I'm thinking you have a bad key switch or bad connections to key switch. This could be why key doesn't turn engine off and battery is not charging. I "believe" voltage from stator & regulator connect to key switch and then charge battery. Bob