Need some electrical help with my ‘68 Plymouth Valiant 100
The voltage regulator is definitely shot
Also the coil resistor is no good,
There is a possibility the the rear wheel cylinders are bad and for sure the front brake hoses are rotted. I ended up buying shoes for the front and rear along with new cylinders for all four.
I'm not sure how you decided these things other than visual inspections. The visual/physical inspection is a fair way to decide on the condition of the brake hoses and the coolant hoses.
As far as the wheel cylinders go, take the drums off, clean and look at what you have there. Leaks can be seen. Do not step on the brake pedal with the drums off! A wheel cylinder than is not working (rusted) takes a little more investigating. I encourage you to do all this first if possible. Two reasons: Quality of new parts generally is junk to will work OK. Replacing wheel cylinders is going to involve removing the fittings from the lines. On the front you will have to do some of that anyway - I'll grant that. On the rear its to the hard lines and it is sometimes a challenge in patience, some finese, and a bit of luck to remove without twisting or breaking the line.
Coil and ballast resistor. Ballast resistor is easy to check with a multimeter. Most of the new replacements wrongs have the wrong resistance. Coil can sometimes be a little trickier to know it was the cause whe nthe engine fails to run. I only read quickly and didn't see a mention of engine failing to run. If the engine ran, then the ballast resistor an dcoil are working.
Voltage regulator. A lot of really good guidance in this thread but a couple of misunderstandings of the mechanical regulator were posted. They are adjustments on the standard ones. They are done under the cover. Your shop manual explains how to do them. Also explains how to do some quick checks to see if it needs replacing. If both fusilible links are in place, and the resistors aren't burned out, then its probably OK.
Alternator. The new replacements often cause problems for various reasons including drawing too much field current. Again maybe I missed it but flickering lights is not enough for me to say 'alternator'. I would suggest that when you are ready to take some voltage measurements with the engine running. Use that in combination with observing the ammeter (labelled 'alernator' gage).
What you can do for now is make use of the ammeter to see what is going on with the charging system. The fact the battery started the car suggests its probaboy OK for now. The only thing I would do first is make sure the battery is fully charged.
Ammeter. The ammeter is in the line between the battery and the main junction for all the power except the starter. When the engine is not running and something is turned on the battery will discharge. Electrons will flow through the ammeter and its needle will point slightly toward discharge. After the engine is started, if the alternator is working properly, the ammeter needle will show charge for a few minutes and drift toward neutral. During normal driving the ammeter should show zero. If the alternator can't supply electricity the battery will do it and the ammeter will show discharge. Then you know there is a problem. How much the needle moves in relation to engine speed and electrical demand will be additional clues to what isn't working properly.
Fuses. Not every circuit in the car is fused. Many circuits share fuses. Dana has already described the fuses so if stuff is working, the fuses are OK, although it doesn't hurt to clean any oxideized and dirty connections. Connectors in the engine bay, including the firewall bulkhead connectors get the harshest environment. There's several threads about how to remove and clean them, when you are up to it.