As Eddie as so swiftly informed you your problem is sadly very common.
Regarding the wiring harness, these are available from the UK as the Douglas Club does get them made to the original pattern.
I may be able to dig out a battery box from the depths of my garage.
If you are interested in either please email me directly via the email ikon below my name.
You should also consider joining us in the Club, incidentally, traditionally called The London Douglas Motor Cycle Club Ltd, which for a great many years has covered Douglas owners world wide, the name is retained in it's entirety purely for the historical tradition of being formed in 1928.
We also supply both the illustrated spares book and the original T35 works manual, I happen to know this because I look after the reproduction and selling of them!
Enjoy your recent purchase, incidentally if you can give me the frame, engine and gearbox number we can trace the history of the bike as far as the distributor. After that we can only track it if previous owners have fed the details into our machine register.