The MGA came with a new wiring harness that was mainly just lying in the engine compartment mainly disconnected. It was unclear which electrical components worked and which did not. I took it completely out when doing the work on the engine and painting the compartment. There were two main parts to getting the electrical system going. First, make sure all the components were working, then putting in the harness and hooking it all up.
The steps for part 1 included buying a new starter (cheap to purchase and easier than cleaning up and replacing the brushes in the old one), cleaning the armature and installing new brushes in the Lucas C40 dynamo/generator , refinishing the heater and making sure the fan motor was working, cleaning the contacts on the turn signal flasher relay box, cleaning the contacts and wheelhouse grease to make sure the windscreen wipers were working (and adding new rubber mounts for the box), putting in a new brake light switch (it is activated by pressure in the brake hydraulic lines and these seem to fail regularly), and replacing the aftermarket control box with an original Lucas one. Although this all takes time, it is rather pleasant work!
Below is a photo journal of this part of the electrical work.