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.
There is a very good article written by David Read. it is entitled "The Electronic Remontoire" published by AHS in 2011. Your movement is very similar to the Reform movement - although the Reform is higher quality.
The 4.5 volts flat batteries are still readily available, so there shouldn't be the need to convert to a battery box. A very common issue with these clocks is that the contacts made when the spring winds down are dirty. You should also check that the coil has a finite resistance. From memory it should be around 5-10 Ohms.
Let me know if you have a problem with the coil. I'm pretty sure I have a spare that you can have.