Tecumseh 10HP Snow Blower Engine Voltage Regulator to Charge Battery

I have an old snowblower with a 10HP Tecumseh engine. It had a 110 volt electric start and a headlight that was powered by the engine. The headlight is an 1156 Automobile 12V bulbin a housing with a glass lens. I am using the engine to power a hydraulic log splitter I built. I replaced the 110 volt starter with a 12 volt one and use a lawn tractor battery to start the engine. Everything works fine but I want to find a way to charge the battery using the engine stator output that previously powered the headlight.
 
I checked voltage from the wires to the lightbulb - At full throttle I get 7.2 volts AC across the light terminals with the light on and 19.2 volts AC between the 2 stator wires with the light disconnected. I am looking for some advice how wire a rectifier / voltage regulator to the 2 stator wires to be able to keep the battery charged ? Also do I need to install a fuse on either the stator wire going to the rectifier or the rectifier output wire going to the battery or both and how many amp fuse would be good to protect the stator from over current ?
 
I would appreciate any advice from someone who is familiar with small engine battery charging circuits.