Grounds would be my first guess. Do you have clean dedicated shiny bare metal ground wires and cables and mounting points connections everywhere they need to be? For example between headlight switch and dash? (you say you replaced your dash...freshly painted? Headlight switch needs to be mounted securely to BARE metal...not painted metal). Same bare metal between bright light switch and floor? Same paint scraping routine at the bolted connections between dash and body? If you did not...did you add a clean dedicated ground wire somewhere between dash and body with paint scraped off? Proper straps/cables between body and subframe? Subframe and engine? Subframe and Radiator Support panel? Battery and engine? Was your dash removal part of a vehicle restoration? Common mistake: If any of the dash or parts of this car were fully repainted, did you take the time to COMPLETELY remove/destroy your beautiful new paint job down to shiny bare metal at EVERY electrical connection, ground, and switch mounting point? This is critical. Nothing kills electrical systems like an over-restoration including fresh paint on everything...you gotta grind and sand that pretty new paint clean off the car at key locations before reinstalling some components...
2nd guess would be a bad hot wire connections or even a bad switch (do not assume your replacement switches are good...might be smart to test them with an ohm meter and make sure they provide zero ohms when contacts are closed.)
Is it doing this when car is running only? Or also when car is shut off and you're testing lights only with the battery. If while running only:
3rd guess would be voltage regulator. When your lights are dimming and flickering, what is voltage doing at the battery on a meter? If it's fluctuating or dropping here while vehicle runs, likely you have a voltage regulator problem.
4th guess would be alternator. Test alternator for proper operation.
