I have 4 Apple M0100 mice, and only one of them is compatible with my Apple IIc. There are plenty of references online to how some are compatible, and some aren't, but nothing definitive about how to identify them, or what is different about them. So I opened my mice up, and the 3 that aren't compatible are all the same internally, and the circuit board identifies them as made my Mitsumi Elec. The 1 that is compatible is made by Alps. Externally the Mitsumi mice have 2 screws, the Alps has 1 screw. Hopefully details of any other variations can be added to this discussion.
Part numbers on the cords are also different, and that probably matters, as the circuit boards have different connectors. The circuit boards have a single IC on them, for the Mitsumi it is a µPC339 quad comparator (AKA LM339), for the Alps it is a 74LS14 hex Schmitt-trigger inverter.
To try and better understand the compatibility problems, I drew up some schematics of both mice in KiCad.
The big difference is the µPC339 is an open collector output, and is using 3.3K pull-up resistors, compared to the push-pull output of the 74LS14. It is already pretty well known that the compatibility can be fixed with a push-pull buffer, and there are adapters that do that available. If you aren't handy with a soldering iron, or don't like the idea of modifying your vintage Apple mouse, you might want to stop reading now and go get one of those.
I did try swapping the 3.3K pull-up resistors for 1K, but that still didn't work. I was checking the voltage with my oscilloscope, and even with 1K pull-up it was barely budging the inputs on the Apple Iic that are also connected to the NE556. It might seem problematic that substantial pull-up current is needed, but I suspect it just needs to get the NE556 trigger past a threshold or something, rather than constantly needing 10-20mA or the likes.
So I did a search on Mouser, for quad comparators in PDIP-14 package with push-pull outputs. There is the TLC3704IN, which is pin compatible with the µPC339, very similar specifications, but with a push-pull output that can source or sink 20mA. Currently $2.39 each at Mouser TLC3704IN. I swapped out the µPC339 for one of these, removed the 3.3K pull-up resistors, and it worked! I've now modified all 3 of my Mitsumi mice, and have tested them with my Apple IIc, Apple IIe with mouse card, and Mac Plus.
Here is a picture of the bottom of the Mitsumi board with the pull-up resistors removed. It isn't entirely necessary to remove these resistors, but they are redundant with this modification and will be wasting a few mA of current.
Part numbers on the cords are also different, and that probably matters, as the circuit boards have different connectors. The circuit boards have a single IC on them, for the Mitsumi it is a µPC339 quad comparator (AKA LM339), for the Alps it is a 74LS14 hex Schmitt-trigger inverter.
To try and better understand the compatibility problems, I drew up some schematics of both mice in KiCad.
The big difference is the µPC339 is an open collector output, and is using 3.3K pull-up resistors, compared to the push-pull output of the 74LS14. It is already pretty well known that the compatibility can be fixed with a push-pull buffer, and there are adapters that do that available. If you aren't handy with a soldering iron, or don't like the idea of modifying your vintage Apple mouse, you might want to stop reading now and go get one of those.
I did try swapping the 3.3K pull-up resistors for 1K, but that still didn't work. I was checking the voltage with my oscilloscope, and even with 1K pull-up it was barely budging the inputs on the Apple Iic that are also connected to the NE556. It might seem problematic that substantial pull-up current is needed, but I suspect it just needs to get the NE556 trigger past a threshold or something, rather than constantly needing 10-20mA or the likes.
So I did a search on Mouser, for quad comparators in PDIP-14 package with push-pull outputs. There is the TLC3704IN, which is pin compatible with the µPC339, very similar specifications, but with a push-pull output that can source or sink 20mA. Currently $2.39 each at Mouser TLC3704IN. I swapped out the µPC339 for one of these, removed the 3.3K pull-up resistors, and it worked! I've now modified all 3 of my Mitsumi mice, and have tested them with my Apple IIc, Apple IIe with mouse card, and Mac Plus.
Here is a picture of the bottom of the Mitsumi board with the pull-up resistors removed. It isn't entirely necessary to remove these resistors, but they are redundant with this modification and will be wasting a few mA of current.