There is an easy fix here. If you are only interested in voltage sags, which is the biggest problem, then you can buy sn inexpensive digital voltmeter with a max/min function. Set up the voltmeter for AC Volts, connect it to the power amp line cord, and play your stereo. The voltmeter will record the lowest line voltage it finds. If one comes along which is lower, then it will note the new low.
I would be concerned if the voltage drops more than 5% below nominal when the amp running but not playing. At a 10% drop, you definitely have a sound problem.
This won't tell you of the duration of the drop, which is the other variable you will want to know if you have a 5 or 10% drop, but if you don't have at least 5%, then you don't need to know the duration. It is a very good first pass check of a potential problem.
Just be careful - the AC Mains voltage can kill you! You may wish to make a dedicated test lead set for this. You can buy one, but they are more money than you need to spend for this. Be sure you check the voltage at the amplifier end, not the wall socket end!