Welcome to the Team Eric!
Dimming lights indicates a voltage drop which with both your battery (what your car was designed to run off of all the time) and a 120 amp alternator pumping out 12.7 to 14.3 volts while the motor is running makes me think your car is one long train or brain dead person texting so he misses a turn light at the stop light away from a car fire. I suspect your wires are shorting out, not having a bad ground.
It could be inside the light switch (you have two, one in the dash and the high beam selector switch on the toe board where it belongs). It could also be associated with your turn signal switch inside the steering column. You have a lot of power going to ground. Since you have about tripled the current capacity of your factory wiring and switches by way of the new alternator your wiring is suspect.
Wiring is always suspect in these cars as the PCV plastic insulation used to coat the wires is dried out and brittle. Any hard bends in the wiring results in the insulation cracking exposing the wires to the car chassis (ground). That is a fire hazard.
Considering the price of replacing your car compared to the price of the light and turn signal switches, I would replace the switches first. If that doesn't work I would then buy new wires from American Auto Wire as they sell OEM wiring that is plug and play (terminated, the correct length, and labeled as to where it goes).