Unlikely.....
If your Alt or Voltage Regulator is crapping out, your voltmeter light should be lit up as well, beside the brake light. And your voltmeter guage should be below 12 volts.
AND, if your Alt or VR is crapping out, your battery would not be functioning after 3 weeks. If the Alt is crapping out, then it should not be charging your battery & your car should not be running. If the VR is crapping out, then sometimes it can be overcharging the battery. Another good way for it to die.
As mentioned, if it's JUST the brake light, then you have a problem in the brake system somewhere.