Searching for 12v switched power after ditching ballast and installing aftermarket electronic ignition

By "switched 12v", are we to assume you're looking for hot in run AND start? Or just in run?
The ignition switch (which I assume you're still using) does not have an output that is hot in both run and start, they are two separate circuits- "IGN1" (run) and "IGN2" (start). When adding aftermarket ignitions (or in your case, a relay) these two feeds are generally connected together to supply a "constant" switched 12v source.
But since you have already sliced and diced your harness, you may have eliminated one or the other already- you'll have to go back and reinstall one or the other if necessary. If you have eliminated the ignition switch (running switch functions through a toggle panel), you'll have to figure that out on your own dependent on how you rewired the thing.
NOTE: IGN2 is hot in start- but it is NOT the starter circuit and is not run off the starter relay. Running your ignition off of the relay could cause backfeed issues that do not allow the starter to disengage, and can introduce other wonky quirks into the system.
And that really looks like an MSD box, not a Mallory.
Hot in run and start.

Yes, still using factory ignition switch, there are no toggles for anything.

The only wires I removed ran from starter relay to either ballast resistor, EGR recirculator, or the factory electronic ignition box, nothing to the actual bulkhead connector was removed removed from the harness. The starter relay I have pictured only has "I" for ignition", "G" for ground, "BAL" for ballast (which I removed), "EGR" for exhaust gas recirculation (which I removed), "SOL" which never had anything if I recall correctly (or maybe because the harness is out of the car I am not recalling what goes there), and the power stud. How would I connect run and start using this type of starter relay? Would the BAL be IGN 2? Electrical is something I diving into as new territory, so explain to me like im a 5 year old

And its definitely a Mallory box. I don't know of any MSD box model that ends in an "E" as seen in the pic, other then the Mallory hyfire 6al that is pictured, but maybe I need to learn to the read the parts I have before learning electrical?...LOL