To start,
Each
in turn (as in, not all disconnected at once), disconnect, clean, then reconnect all of the connections to/from the battery, alternator and solenoid. There can be visible hidden corrosion that robs voltage, current or messes with sensors (an eraser can remove the fine layer of corrosion from contact surfaces to make them nice & shiny clean). Also the disconnect, clean and reconnect for the car's body ground (likely a cable from the neg battery terminal out to the body aft of the solenoid, or even on the spring tower). And you may have a sensor or ground issue back at the gas tank (tank senders can be an issue with Eagles). I assume you cleaned the battery terminals and clamps to nice & shiny, then re-clamped the cables onto the terminals. I use dielectric grease on all connections to minimize future corrosion.
I assume the alternator pulley was the same, or you used the old one? Belt correctly tensioned?
Then see if the behaviour changes.
Soldering a wire is not recommended, as vibration can break the wire strands were they meet the solder, causing a later failure. An insulated crimp connector is more reliable - IF you use the correct size crimp and the proper crimp tool (not pliers, not vicegrips, etc.). Also for breaking under vibration, don't use solid conductor wire in vehicles; use stranded wire.
In future, there's also different alternators that fit in Eagles. The 94 amp one is popular. I have a reman of that.
My old notes:
AC-Delco 12SI clocked @ 3:00
94 Amp: AC Delco part #321-266, Lester(cross reference) #7294-3, BOSCH AL559N (N for new)
Application: 1984 CHEVROLET CAMARO 5.0L 305cid V8 4BBL (G ) with A/C, amperage 94, regulator i/r, clock pos 3, pulley class 1979452, voltage 12, rotation cw
Any Lester # ending in 3 should have the same wiring connection position as the recommended one from the Camaro.
78 Amp: Lester #7278-3, will have the same wiring connection position.