You need to change out some connectors.
On solenoid board - replace plug on J3 and ditch that old IDC type connector.
New plug = Molex 22-01-2257 (obsolete) or CS100-25-LR.
You can find CS100-25-LR, contacts (08-52-0123) and key (15-04-9209) here:
The wire that he spliced onto belongs at location 10 within the new plug.
Replace entire set of plugs going to rectifier board:
Contacts (08-52-0113 or 08-52-0072) and 3x keys (15-04-0219)
These can be found here:
They probably soldered it because 20 pin plugs used to be somewhat difficult to find.
You will need to replace the PC board mounted headers on the rectifier board. The existing ones are either burned or damaged due to previous person soldering wires directly to the header pins. New header = 26-48-1241
You would need two of these to replace the existing headers.
Alternative to replacing header pins is to replace rectifier board. Can get new ones but don't spend more than about $70.
For good info -- see here:
And especially here: