This is a fairly old GMC Chev Cavalier with a 3.1 MFI V5 engine.

The car start behevour differently from about 2 months ago, the main
thing is that all the light (headlight, interiorlight, panel light, et
al)go up and down at about 1 Hz.  It always do this when the car was
started from cold, and sometimes, it goes away within about 5 min of
driving, and sometimes it stay that way for 20 to 30 min.  It come up
less often when the car is warm.

When the lights go up and down and the car is at idle, the engine speed
fluctuate within 200-300 rpm (both cold and warm).

It appears that the lights fluctuation is due to the engine speed no
stable.