Hello!
I have recently put my hands on an old Japanese cassette player and pulled out an interesting motor.
It is labeled as DC 7.5V MMI-6U7HW SINGAPORE. It has four wires, so it would suggest a stepper.
Turns out that it isn`t, red and black wires, when powered, spin the motor continuously, so it is a DC motor.
Blue and yellow are probably some sort of sensor\encoder\tach? But how to check it? And how to use it?
Maybe it can be used ti count pulses?
Aunt Google told me that it might be a Matsushita/Panasonic DC motor for cassette decks.
I could not find the exact label but some close to that.
The second wire pair might be either for speed dubbing (with a switch connected) or might have something to do with speed control via a potentiometer or your thought about the speed feedback might be right.
If you still have the old cassette deck, it would be a good idea to either check for data about the cassette deck itself and/or have a closer look at the place where the motor wires were connected to.
I think, if you have got the name of the cassette deck model, go and see if you can find someone in an audio vintage forum to answer your question about the motor.
Good luck.
Second pair of wires are probably a tacho for speed feedback.
I didnt get how to use second pair, so I wont use it for now.
At least you can check resistances between all wire pairs and any voltages these mistery two wires may output when motor is powered. See what comes out.