I don't own any Mighty SOS engines, but I can give you some general guidance. The 3 wires top to bottom are LIKELY center roller, ground (outside rail), and chuff switch. This is based on the trace sizes and that the ground connections often run around the periphery of a board. YOU NEED TO VERIFY THIS WITH SOMEONE ELSE.
The second problem is where to connect them. There should be another tether coming through or under the cab. In other SOS engines, a polarized 3 part tether was used. You will need either pull off the boiler or continuity meter the 3 wires. One should connect to center roller, another to ground, and the third should connect to ground intermittently depending on the position of the drive wheels.
There should be 2 additional wires (not shown) that connect to the speaker.
You may want to post a picture of the locomotive tether. Hopefully someone who has this engine will be willing to pull the boiler and tender shell and give you correct information.
Bob