This discussion might belong in its own topic, but here's part of the Dancing Dolls schematic (made a couple of months later) and some answers.
Dancing Dolls coin chute (resized).jpg
On the coin door the Coin Chute switch (in red) should connect the orange and blue wires.
The Anti-Cheat switch (in red, bottom left) and Bounce switch both need to be closed for power to get into the transformer.
Quoted from Charles_Kline:I found that the contacts on the "R" "Hole" relay were also purposely bent closed and the coil was burnt up. Checked it with a MM and its shorted, reads 0.4 ohm. Can someone with a Wagon Train let me know what that coil is supposed to be?
The R relay switch (in red, left side) also keeps power running into the transformer. The R relay coil (in red, top) is always on and often looks toasted. But unless you desoldered one of the solder lugs the .4 ohm is likely the resistance of the transformer and not the R coil. Either way the R relay coil in Dancing Dolls is an A-3498 which should have a resistance of about 30 ohms.
The important point though is that nearly everything you're asking about is between the plug and the transformer and is running at 120 volts so I would advise unplugging the game before poking around any of it.
/Mark