Electrical problem with Toyota Avalon '02

I'm having an electrical problem with my '02 Toyota Avalon (91K miles). Trips to the shop have not stopped it. I've changed battery and alternator but still there is the problem When the car is on, every single component (interior/exterior) that is a light source (the clock face, the radio, instruments, headlights, parking lights, etc.) Will flicker in a subtle, but pulse-like kind of way. The lighting never goes out entirely, just quickly flickers from regular state, if I've stopped behind another car you can see my headlights pulsing in the reflection off the other car's tag or rear end. I also perceive a slight whiny/strain type noise from the engine area when the flicker is bad. I'd say this problem has existed on and off for the last three months. Any idea what gives, or what the fix is? Many thanks!