Looking for a suitable transistor for a simple circuit - 50 y/o Junghans clock repair
You say to have found the AC125 transistor, but you don't know which to buy from the four offered. Probably they come in the flavours of different amplification factor.
I would take the most expensive type, with the highest hfe (amplification factor), and lowest leakage. But for this simple purpose probably all four will work, but higher leakage could drain the battery quicker.

Use this one:

http://www.diyguitarpedals.com.au/shop/index.php?main_page=product_info&amp;cPath=3&amp;products_id=4

but I must say that $ 6.00 is not cheap.
An American replacement for the (European) AC125 could be 2N1176 or 2N406 (even same pin-outs), but I think, for the simple purpose it is used, any transistor that is a low power germanium PNP will do.

I saw one photo from an ATO-mat print board, and I could only just figure out that the first character of the transistor type is definitely an A, so the chance that it really is an AC125 is there. I myself have a Junghans W.707 clock, but in there there's a much larger transistor used with no print on it. So maybe that they've used any (low power PNP germanium) transistor cheap in the market on that moment.

Here I found, and re-drawed another (slightly different) diagram. It could be that this is another model from Junghans:
http://www.hwynen.de/jgh-w794.html







simulate this circuit &ndash; Schematic created using CircuitLab

Finally, you have measured the coils, and found them not broken, but see that there is a small possibility that two windings are shorted, and that is much more difficult to determine.