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

First.
You have a '77 Aspen. Many things you may have read about 'all' A-bodies, even if generally true, are different and do not apply to a '76 A body or a '77 F-body.

Second.
There is nothing on the older starter relays that would be useful for your purposes. The starter relay's stud serves as a junction in the battery feed. All the other connections are only for starting.

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My suggestion is to (hopefully) reconnect the factory wiring. Then place a piggyback on the ballast resistor terminal for the on/off trigger of the Mallory box. If the box is a CD ignition, then the ballast resistor itself is not needed - so you could do a jumper. On the hand, it probably doesn't hurt to leave it if its simpler. Only a tiny amount of current goes through it when used for telling a CD box to be on.

I don't have a '77 FSM or diagram. But if its anything like the '76 wiring, the power feeds (alternator and battery) are joined in the engine bay, and the main feeds off of them are branched off in the engine bay. The basic concept of the main circuits remained the same (in '76) as previous years.
Ignition 1 (Wires labeled J2) is on with key in run
Ignition 2 (Wires labeled J3) is on with key in start. Starter relay wire from the key switch is also hot with the key is start (but not directly connected to J3).
Switched Accessory is on with key in run or accessory.

This is an overview of the '76 A-body main circuits.
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