>> The head badge says William Brunner.
It actually says "Brünner" -- but William is not a German spelling anywhere I"m familiar with.

Brünner is a name that could be from Germany, Austria, the Alpine part of Italy -- think Francesco Moser, great name -- and points east, but none of those fit with William -- Wilhelm would be the usuall spelling.
I'd say most likely American, where we mix & match freely.

Nutted brakes + chromed lugs & fork is an odd combination. Add the super short chain stays, I'd say made in the mid-80s as a one-off with parts on hand?