Why had old battery gone bad? Are you sure generator light was working properly to start with prior to the battery swap? With engine running just off idle - what is the voltage measured at the battery. Should be higher than 13 volts.
What year is the vehicle? Early cars around 71’ had a diode associated with the generator light located behind the gauge that could cause some flakiness if it has gone bad. This diode is shown in the Haynes schematics but isn’t going to be shown on the simplified schematic I’m posting below.
Start with ensuring all battery connections to new battery are correct and all the red wires are solidly connected. Likewise, ensure your negative cable is solidly connected to body - chassis ground.
From there this gets a lot more complicated and you’ll need a multimeter to troubleshoot.
Here is Spoke’s simplified schematic. Note on some early cars I think it’s fuse 8 whereas later cars are fuse 9 as shown.
Make sure fuse 8 and 9 are seated and not blown - current flows through that fuse at key on to light the generator light.
As far as the light lighting at high rpms - that is much tougher to diagnose.
For now - start with figuring out why the generator light isn’t on at initial key on. That will likely lead to the other 1/2 of the problem once we verify the fuse is there, the bulb we know is working, and the other portion is in the regulator itself that feeds battery voltage to the alternator field windings at start up to bootstrap the alternator to life.
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