OK, so the starter is not cranking. That really doesn’t have anything to do with the ignition coil or ballast resistor. Those are just for getting the ignition system working properly.
The lack of cranking is either something wrong with the ignition switch, the purple wire, the starter relay (solenoid), or starter, or starter cables.
So let’s do some basic testing.
Let’s make sure what we’ve got going on here.
The positive side battery cable should go to one of the large studs on the starter relay.
Sounds like you’ve got that, but just making sure.
The other large stud has a cable that goes down to the starter. No matter what color the cable is, this is not a negative. This is a positive and gets power to the starter.
But we also need to know what type of starter you have. Is it a standard Broncos starter, or more modern starter with its own solenoid on it?
Sounds good, but we need to make sure there is power to the purple/violet wire when the key is in the start position. We can test that a little later.
So that confirms that you have the battery cable connected. Do you also have the large red Centech wire connected to the same large terminal as the battery cable?
And it should have their 60 amp fuse in the red wire?
Think back then, and maybe still, they used a maxi-fuse and holder with a plastic cover.
Is that what you have?
Let’s test the starter circuit first.
With the vehicle in neutral or park, and the brake applied, (and your nerves intact and ready for surprises) jumper the starter relay to see if the starter cranks.
Be ready to be surprised just in case it actually does crank.
To jumper the relay, take a small bit of wire that you might have lying around, remove the purple wire from the S terminal, and touch your jumper wire between the battery positive side and the small S terminal.
Just doing so I should give you a major click, and the starter should crank.
If it doesn’t, we have more testing to do.
Try that and let us know what you got.