Chris
I struggled for years trying to get a fully up and running Start-O-Matic box. I eventually managed to rebuild one and it worked fine for about 6 months and them stopped working for some reason. I never bothered fixing it because I found a Lister wiring diagram for the Push button start & stop with remote control facility and converted my Start-O-Matic to that system it works fine although I have not connected the remote option yet. This system works really well and I would highly recommend changing to it.
It is possible to just rewire the top box on the generator with a few new components and do away with the Start-O-Matic box completely.
The new components required are
Start button
Stop button or switch
24 volt 2 pole relay 30 amp
24 volt 3 pole relay 16 amp
Stud mount 25 amp diode
Here is the wiring diagram that I created from the original and the original as well.
The original charging system is fine on the lister its adjustable with a big fat resistor in the top box. All you do is set it low to start with and if it does not keep the batteries charged move the slider up the resistor a bit. You will know when you've got it right. Another option I have used in the past when my Start-O-Matic box was non functioning is to use a small switchmode 24volt battery charger for kids scooters like this ebay item no170732365614. It worked very well.
What is actually wrong with your Start-O-Matic box? They are very rugged and most of the components should be okay. The only problem I have had is getting new contacts for the big relay. What parts do you need?
Mick