Good afternoon, Harold!
I have a couple of these. I may even have one, like yours, originally given away by the British American Oil Co. I do believe most of these were gifts.
As you probably know, the concept is pretty simple: the two-ended weight rocker is flipped by an electromagnet to "wind" the clock, and when it rocks back to its rest position, this trips a switch that resets the rocker again. Very similar in many ways to the larger Empire, American Self Winding, etc. clocks.
The battery I have from one of them is 4.5v, and can be easily replaced by a battery holder with 3 AA's in it in series.
Is yours working?
Best regards!
Tim Orr