Your Rodney is a typical HA-1 15 clone. The wiring block in the end compartment was they way those and many others were wired. Nothing complicated or difficult there. The entire wiring block harness is still available from many sources.
There are a couple types of foot controllers. One type will have a spring loaded lever that swings in a arch making contact with many contact points. At each point the motor speed should increase. These contacts can burn, corrode, and pit. The wires to them can also burn out. If dirty, burnt, corroded or lightly pitted they can be cleaned and brought back to life. If the wires are broken or burned through they can also be fixed, but it's better to replace the unit.
You should be able to slide the bottom off of the controller and see the resistance wires and swing arm.
This type comes in a variety of shapes and sizes but this is an example of the type:
The other is a carbon pile type resistor. Most of them can be adjusted as well. And they do have contacts that can become burnt and or corroded. Here is an example of that type:
As you can see both types have only two connectors to undo, so replacement if needed is easy.
The wiring in your picture is typical 50s twisted cord wire. As long as the insulation is good there's no problem using it.
Sew-Classic has both the cord block sets and new standard and electronic foot controllers if you need them.
Joe