Alex,
Douglas advertised a bulb horn that looked more like this:
Presumably a Powell & Hamner (as this illustration is), since they offered their machines with P&H acetylene lighting sets.
These horns started showing up in the Douglas catalog by 1922 and persisted till 1929. I do not know how many years after that it was still available. None of the 1931 models in the catalog are shown fitted with any type of horn, bulb or electric yet they have headlamps and accumulators. The full BTH dynamo lighting system is shown in the options (the pancake dyno is shown fitted to a ghosted S6) for the side-valve machines only, with vibrator type priced at 0-10-0 and the motor driven type at 0-15-0. A Mag. Generator is offered for the F/G31 OHV as a 5-10-0 option, but no mention of any other electrical equipment, though again a BTH headlamp is shown fitted (but not the mag/generator!)
So some sort of bulb horn must have been fitted when electrics were not ordered (surely it was a legal requirement by that time), but the would be purchaser was left to his own initiative. I am sure the local Douglas agent would be quick to offer a range of accessories.
-Doug