I'm looking for a wiring diagram for an old GE Mercury ballast in the old M-250R Crimefighter.  The end of the ballast says:

175W REGULATOR
35-201080-17
(NOT FOR ORDERING)
GENERAL ELECTRIC

It is a large ballast with 4 coils and 8 different terminals.  The coils appear to be all isolated, connected by jumpers from the various terminals.

It look's like Mag-Reg ballast, the heaviest and least efficient (except for tungsten blended lamps), but best regulating. Do you have the capacitor (or it's spec), that belong to this ballast?
Generally for this kind of ballast:
  One coil on one side is the primary, it will have multiple taps (120, 240, 277,...).
  The middle is the regulating one - connection to the capacitor
  The third on the other side with only 2 terminals is secondary - lamp connection.
But when you are not 100%sure, for experiments use some high power (~4..5*ballast nominal) incandescent (or a parallel bank of multiple) as a "fuse", the discharge lamp has to start, the ballast should not excessively heat, the incandescent only dimly glow... Even if the circuity would be wrong, such "fuse" will prevent instant destruction, so you would have enough time to respond (e.g. to ballast overheating).

I'm not sure if that's it.  I'll have to post a pic of it.  Here is a pic of the capacitor.

Here is what I've figured out so far.  There are two primary coils wired in parallel with each other to the mains.  There are two secondary coils jumpered together.  one lead comes off the first secondary, to the socket center.  The second lead comes off the socket shell, through the capacitor and back to the second secondary coil.

The lamp seems to light if either or both primary coils are connected to the mains.

I'll post a pic of the original ballast of my early 60's M-250 just in case it helps....

Edit...OK I posted a pic here. From what you describe, it sounds like a 'CWI' ballast as I have posted.

The mounting bracket is a little different, but the ballast is the same as mine.  Thanks for the pic.  I will have to get a pic of mine posted soon.