checking encoder signal at A/A- or B/B-

To see if a motor encoder is sending feedback signal, I put multimeter leads on the A & A- encoder wire terminals (same thing on the B & B-), then turn the motor shaft. I just assume the encoder is good when I see some voltage reading changing.

Is there a better way to check the encoder with a mumtimeter?

I would use an o-scope and look at the signals. you should get a nice square wave. the a and a- are differential as is the b and b-. the a and b channels will be offset by 90 degrees.

A multimeter will show something, but nothing useful. You might set it to read frequency, and verify if the frequency is correct for a given speed.

That still misses channel phasing, and pulse quality.

An Oscilloscope would be much better, like this, but seriously, an encoder tester like this one is the way to go.

Failure modes for encoders are missing output, and weak LEDs. Phasing is fixed - no need to measure it.
The following is for a 5 volt TTL output version.
Multimeter will show that you have two outputs. Next, check for switching between zero and 5 volts. With weak LEDs, these voltages will be way off.
The other thing you can do is test on the machine. Do this test away from the home position, in case the machine resets the counter at home.
Move 1000 counts positive, then 1000 counts negative. Repeat 10 times. Is the count still accurate? With weak LEDs, or slipping mechanics, this count will be off.
Modify procedure for your machine.

An oscilloscope or encoder tester is still the best method.

Those simple digital counters thats battery powered can also be used to check the signals