The alternator light should still come on when you flip the ignition switch, and then turn off after the engine actually starts and generates power. The ignition switch is just the equivalent of turning the key on.

The regulator/brush is a common issue with cars these old, and I remember buying a generic replacement for under $20 a while back. It's on the back of the alternator and is easy to remove, inspect, and replace if needed. Just two little bolts and I think maybe one wire.

Make sure the alternator is completely hooked up... There should be the main positive power wire going from the battery to the starter to the alternator, and then there's a small wire (I think it's blue or blue/red on my car) that also needs to be connected. It runs up to a two-wire connector in the engine bay (along the firewall on the driver's side, around a bunch of other wires) before it goes through the firewall; the other wire in that connector is the starter signal wire. If this alternator wire is not connected, the alternator light on the dash will never come on... not even when you turn the ignition on.