I'm back to this again!
Took the alternator to have it tested.
It passed the Lamp/Diode Trio test
It passed the Rectifier test
It failed the Regulator test (which my guess is, it failed due to the regulator is external)
Here is the printout.
Battery Volts- High 15.7, Low 13.7, Actual 13.36
Ripple Volts- High 2.0, Low 0.0, Actual 1.85
Lamp on volts - N/A
Lamp off volts - N/A
So...Alternator seems okay. Still don't know why the car is cutting out when lights/radio etc are on.
Should I start a new thread on this since it's not related to the light relay harness install?