A look at the show reports for the end of 1911 (November) indicates that the enclosed ZE-type Bosch magneto was being fitted to Show models and offered for 1912.
I suppose the serial number of the mag would give a clue if it's original or not.
Useful to have the original poster chip in - do any of the cast parts have 'REX 1912' on them, and is it the 499cc or 532cc single?