Well that is looking promising. These chargers are worth quite a penny I notice, especially during winter when they are really needed.

I figure "JMP Relay_6" goes to the orange pair, and "Pri-con" goes to the grey pair. This is opposite of what you have drawn? so I'm not sure what is going on. It's not a big problem - when it's in 300A engine-start (high tap) the transformer will growl and be loud. If that is mixed up (relay connectors), on the 15/60A setting it would be in 300A mode instead and you should hear it growl. Or it's in 15A/60A mode when it's in 4A mode, if that is flipped. Both relays off is 4A trickle charge I believe.

Or... With the relay cons not plugged in, I would measure the relay connector voltage i.e. +6VDC or 0V between the two pins (do not short out), when switching say from 4A trickle to 15A/50A mode and that can ID which connector is for that relay.

There is a tiny chance the burnt diode happening also damaged the control board output for that one relay. So the relay coil may never get power, or always be getting (stuck) coil power. No biggie, it's just a small transistor on the control board that ends up driving each relay output. If you think the charger's output power is not matching what you chose.

One question - what does the big (+) output cable connect to? I can't see it in pics. I can't find what they did with the transformer center tap with ends up being positive out. The (-) output cable connects to the heatsink I think.

Maybe I'll just post the schematic so far. I couldn't figure out the last bit, the hairy secondary wiring 8 wires eek it was too much to decipher. Very scary.
edit: adding a draft schematic, will update it here as corrections are made.
View attachment 362473

Further testing shows 6v across "pri-con" connector when set to charge @ 24v and connected to 2 12v batteries in series.

Question still remains: which gets connected to "pri-con", orange or grey?

 

My guess is "pri-con" means 'transformer primary control'. It is the tap change relay for low/medium output... voltage I guess like 6&12 or 24V (mode) requires. I think how it works is the transformer output is switched to a ballpark and then the control board regulates it down.

Pri-con should always have 6VDC power on one pin, and the other pin gets grounded or not by the control board to turn the relay on. So with a relay connected there, you should see 6V (24V mode) or 0V (6V mode) across the it, and hear the relay clink. My guess is to the grey relay wires is PRI-CON.
If it's not happening then the relay driver transistor on the control board could be toast.