I did have the same bike years back it went well.
Yes it did run with no battery .
But I never had elec probs with it at the time .
Is the earth wire ok on the frame ?
I've had times when the spark plug cap has been pulled off over and over and the cap to coil lead is chewed out , I just cut 10mm off the coil lead and re fit cap sometimes its the little things .
That's about all my elec back ground