Hi shipmate!
i`m no electrician but red wire to the positive tag on the motor and green to the negative tag,usually there is a red dot indicating the positive tag.
esc looks like a home made jobby!

Bottom line is to go modern with the ESCs. Put the old ones on display, in a box, whatever. They are just not usable in a model boat. My first speed controller (circa 1972) was home made and had two 3 position switches. One had power resistors, and the other fwd, stop, and rev. It got quite hot controlling the 6-volt automobile heater fan motor.

Lew
Florida😎, USA

Hello, I also installed 2 mechanical speed controllers in the ocean tug "OCEANIC" Ware. Worked perfectly, but they were power guzzlers and they got hot. That's why I kicked them out. Here's a link to my controllers.

https://youtu.be/H7adADtY6gE?si=xkxbMSdCsD7CvVGd

Over here in Canada, we referred those rheostat friction controllers as Bob's Boards.
They are simple, resistance type controllers, very inefficient, as voltage not used(partial throttle) gets burned off in resistance.
Any of the modern ESCs are digital, and the circuitry allows any unused voltage to be returned back to the battery.
The price of the newer Controllers and reliability makes them the way to go in my humble opinion.

If you're disposing of it, my vintage stuff collection would like to have it join the various oddments in the box.
Cheers Colin.

Good evening, the wires go to the sweep arms as in picture. I still have 3 in use from the 70's. Have a tendency to get hot.
Cheers Colin.

Cheers Doug, that makes sense 😊

I'd start "dry testing" it. Connect the servo to a suitable output of a RC receiver, apply power to it, and check if the wiper moves when acting transmitter's control. Check movement limits, too. It seems that the wiper can move 180º, but 90º should be sufficient.
If all is OK, you can add a suitable motor and its battery (if different from the one powering the RC receiver). And check if the motor moves, and if speed can be controlled.
Motor shall have the same voltage rating than the output of the battery (don't plug a 6V motor to a 12V battery)

Hi Doogle,
What you have there is a Varispeed Board from Bob's Models.
Commonly known as 'Bob's Board'. Still have one in the cellar somewhere.
Took it out of the Sea Scout my Dad built in the early 60s.
ARL is not quite right🤔
The Red and Green wires, going to a Tamiya connector, go to battery + and - respectively.
(Don't forget the switch and fuse!👍)
The motor wires are connected to the two copper wipers driven by the servo.
Attached vid (link) shows how to assemble and wire up the board.
As ARL says they are very inefficient as battery power is dumped into the resistive track at slow speeds. Which heats up the tracks.
Max current is 8Amps if I remember rightly.

Maybe Colin would take it off your hands, for a Bob😉, to add to his vintage RC display?
Cheers, Doug 😎

Thanks Fred and ARL, I'd taken the esc out originally as it wasn't wired in - the wires had been cut, but I don't like throwing stuff out. Thought I could bench test it if I knew what was missing 😕. A photo of the boat it came from 😊