Hyundai Repair: Dash light + Clock electrical issue, accent gsi, long periods of time

Question
I recently purchased  a 2001 Hyundai Accent GSI sport. The clock light seems to flicker (dims and gets brighter) without any direct connection to bumps. The dash light seems to be connected to the issue as when the headlights are turned on the dash board lights will go on and off for long periods of time.

Answer
The clock is connected, along with the other dash lamps, to your rheostat (dimmer switch).  If the outside tail and parking lamps turn on and off along with the dash lamps, you'll need to investigate the tail lamp circuit as the root cause of your problems lies in this circuit.  If, on the other hand, the exterior lamps remain at full brightness, the problem is almost certainly with the rheostat.