Faint buzz in speakers

If this was my system, it would be rewired, use different outlets. If anything is 2 prong, instead of 3 prong, swap the cord around. On 2 prong power plug, swapping the plug around can have profound sound differences. 

Of course make sure there are no lights turned on, on that circuit, signal cables are away from power cables.

Might also be your amp needing some service, like bias adjusted, or a component going out of spec. 

"simply make sure all lights with dimmers are turned off while listening”

"I noticed that sometimes it's a light rheostat (sorry, dimmer switch) making noise in the circuit. However, it's usually a cheap charger that is the culprit in the circuit. "

- better amp designs are immune to AC power harmonics, introduced by fast switching currents. so far I found Accuphase is the best! 

"it turned out to be proximity to a router. "

- I had similar issues before changing pre/amp to Accuphase.. to identify RF noise immunity issues, just touch/move arm to diff components and cables, around amp/pre/turntable/CD etc at max loudness (TT/CD/etc idle).

OP. From your updated description, there is absolutely nothing wrong with the amp - its just regular residual noise. Forget about it and enjoy the music!