Vintage Dirt Bike Q & A

Getting the last few thing figured out with this bike an mt250 doing the wiring now. I had it all hooked up and the bike was running so I switched on the headlight. It came on fliped between hi and low and they both worked fine. I left it on low and let the bike idle for a few mins. The low beam went out and a small puff of smoke came of the resistor mounted by the headlight. I turned the bike off and then being stupid stuck my finger on the resistor to see if it was what had gotten hot, it was now I have a nice burn I then started it again and put the high beam on which burned out a few minuetes later. Now I know this bulb runs right from the stator the book says it runs off ac current not sure how this works but thats what the book says. What I want to know is it normal for the low beam to short to the frame thru the resistor when the low beam burns out. The hot wire goes to the low beam and the resistor at the same point so it seems like this would be a normal thing for it to do if it burned out but I am unsure. Also does anyone know if you have to have the high beam indicator bulb working to keep the high beam from burning out as its in the same circut?