Hi

I had the same exact problems with my indicators and headlamp as I am rebuilding mine too.
As said by eggsy01, you will have to unplug one of the wires because otherwise they will stay on. I believe there are three wires but you just need two.

Try to give the kickstart a few kicks. My headlamps went on after the third kick.
I have no idea why because I had a fully charged new battery too.
I even bought new headlamps which are extremly expensive.