It looks more like a Bally transformer to me than Gottlieb or Williams. Fortunately Bally often includes some transformer details in their schematics like this one:
Bally transformer (resized).jpg
You might browse through some of the Bally schematics on IPDB.org to see if there are patterns or common configurations.

Your resistance measurements tell you something about the relative number of windings between the various pairs of terminals since more resistance would indicate more windings.

If you're comfortable working with electricity and are aware of the dangers and safety procedures you could also apply a small AC voltage from a wall wart or variac to the various terminal pairs and measure the AC voltage at the other terminal pairs to confirm the relative number of windings.

As an example imagine that the transformer has a primary winding intended for a 120 volt AC input and a secondary winding intended for 50 volt AC output. If you apply just 6 volts AC to the primary winding you should see 2.5 volts AC at the secondary winding because the ratio from input voltage to output voltage will stay the same (120/50 = 6/2.5).

Even though you're using small voltages though you still need to be careful. If you instead apply 6 volts AC to the terminals intended to supply 6 volts to the lights, you'll probably get 50 volts AC and 120 volts AC at the other terminals. (see https://pinside.com/pinball/forum/topic/how-do-you-test-your-light-sockets-with-the-machine-disassembled#post-5976888 for details.)

/Mark