The starter button disconnects the headlight when cranking the engine on your model. There is a clear piece of plastic behind the starter button that degrades with time and yours is likely missing. In fact, I'd guess it broke and the PO removed it. Without that piece of plastic, the starter switch will not work and apparently a connection has been lost to your headlight circuit. The best solution is likely just to get another switch. I recommend against buying used ones for your bike because a few plastic Internal parts will likely be broken, or ready to break, in whatever used parts you buy. You can find new ones on eBay and at various parts houses.
Camelman