Any electrical guru's know off hand what these are for?

The washer pump got only one wire, brown I think. Wasn't the only brown wire though so wiring diagrams and testers are required.
That white engine harness connector was added for nothing more than ease of assembly at the factory. Wires melting there is somewhat typical. Delete it.
The wires in it are blue and green and black to alternator, purple to temp sender, and more. the blue to alternator has a branch that went to a electric choke assist that can/should also be deleted. It's not required and the controller for that choke heater is surely old toast.
Previous owner(s) have been dealing with this cars electrical short comings and failures the best way they knew how. You have opportunity here to properly repair it.