These are good controls, the world has moved on to other ways of doing things, but they are simple and bulletproof. My farm house has a very similar setup but with a newer controller and cistern due to low well output. Some tips from my experience:
Hard water deposits will coat probes and eventually shrink seals so that conductors corrode away, so check those.
You can use an additional probe as the neutral return path, and it's probably required if your tank and piping aren't metal. It's very reliable that way.
If you need new wiring, B/W sells submersible wiring, probes and kits in various configurations for cheap. We just suspend the probes and hang them in the tank. Makes level adjustments easy and wiring is very thin compared with pump wire.
Make sure wiring around contacts in the enclosure doesn't interfere with their physical movement. It's easy to think something is faulty when it is just blocked from working right. Ditto for dirt, etc.
Make sure that you have the right voltage for the probes, it depends on the makeup of the water and it's hardness.
A new B/W controller may well mount right up to the existing enclosure if you want to swap.
That's my two cents. I'd be interested to hear how you end up doing this. I went with this system again as it had worked well for 50 years and we just wanted additional functions. But my industrial/controls knowledge is about 50 years behind, since that is what I see and work on with basic farm systems here. Seems like every time I try to modernize it ends up being more expensive, complex and lesser quality than copying the original. :blink: