Thank you for the suggestions!
FrankBuss I don't have an oscilloscope, yet. :-) The Siglent is in the mail right now, travelling :-)
SeanB, I opened the encoder and its a 24 pulses per rotation. You can actually see the small contacts.

I did not know how it worked but now its obvious. All the contacts were very dirty and oxidized!
I cleaned the rotary base and the three contacts. It has three copper contacts that are forced on
the rotary plate with just the tension of copper itself! Very bad design. This thing is destined to fail!
Anyway, I cleaned it, re-tensioned all the contacts and made sure that they had the right distance
from each other. (I cut the width on one of them shorter because they were almost touching!)


I reassembled the parts together and made a small video to show some small test using two
multi meters in continuity mode. (Sorry for the very annoying sounds...

)
I think that this is an easy way to quickly test a rotary encoder, although it does not tell anything
about the 90 degree phase. Maybe if you can analyse the sound of the beeps using a steady
rotation speed, you can find out the phase between them. I am not sure.
I will try now to solder it back on the board and reassemble the stereo.