G Electrical Problem

With 6 volt you need to have very good connections, I would check those first or leave the 6 volt hooked up for ignition and hook a 12 volt up to the starter to turn it over, they aren't nearly as picky about making good contact. at least you might find out if it's in the starter or the wiring?

Put a volt meter on the cable at the starter, see what it reads with the starter engaged.

The 6V system is a very simple system, BUT it needs a little attention once in a while to keep it in tip top shape. Cables were mentioned, but make sure all grounds are clean and connections are also clean. Very important! If the system has its grounds and connections are clean, I would pull the starter and have it tested and inspected. Don't forget about the Battery either. Doesn't matter if its new or not. Do a draw test on the Battery FIRST! If the power supply passes a draw test, then move on. May save you a lot of time. We offer the Pertronix electronic ignitions in 6VPG, 12VPG, & 12VNG. We also offer a wiring system kit for a 12V conversion for the G if interested. Double check your Battery, connections, & grounds first before you do a conversion. Could be a simple overlooked problem....

After owning a G for a short time, I see no reason whatsoever to change to 12 volts. That engine will spin over fine with 6 volts if you don't have other problems.  If the tractor has sat for a while, pull the starter and jump it with your 6 volts. Check for mouse nests in the flywheel housing. If you have good clean connections to your battery and the starter switch is good, you probably have bad brushes or worn bearings in the starter.