Intermittent loss of electrical power on a Ford Mustang

This is a 1999 Ford Mustang GT 4.6.

Electrical power completely shuts down and comes back on, the dashboard lights and gauges go crazy.

I put in a new battery, alternator and negative cable and haven’t change the positive side yet. I also replaced the ignition switch, key, wiring harness that plugs into the alternator’s voltage regulator. The battery gauge on the dashboard drops real low when it’s doing this and then it comes back up to normal value again.