OK, without the diode, the battery is allowed to discharge back out into the alternator. Hope it has not be dammaged.
Red wire is your charging wire and should have a rectifying diode to stop backflow. Black I think is the light circuit. Since your wire was cut off, I bet that diode is gone. Few options
Replace the pigtail with the diode. (Briggs & Stratton : 393456)
Link to one on Amazon
. There are some cheap ones on Ebay too. If you have the other end of the plug great, if not you can tap into the plug pretty easily with a couple round plugs.
More moderate and cheapest, purchase a diode and solider it into the red wire.
I believe it is a 6A, 50V Rectifier Diode. Can be Googled
Hope that gets you on the right path.
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