The Neos Mouse was a third party mouse, produced by the company Nihon Electronics Co. Ltd. (internally Mitshumi), introduced in 1985 for the C64 and C128 at the same time as the Commodore 1350, really a joystick shaped in a mouse form. (Edit: the 1350 mouse is inside a Neos mouse [1]).
It went inside a drawing package named "Mouse cheese" but had poor support by other software as Commodore launched in 1986 their 1351 real mouse.
Curiously similar packs existed for the MSX (Mouse+Cheese), Amstrad CPCs (Mouse Pack 2.0, Gerdes Mouse, Centaure mouse, ASS Reis-Mouse or Reisware-Mouse) and even the Enterprise 128 (Boxsoft's Paintbox). The reason was that in reality the Neos mouse was an MSX protocol mouse with the pins interchanged to suit the Atari standard.
MSX DB9 has the +5v in pin 5 and ground in pin 9, but the Atari DB9 standard (Amiga) has the +5v in pin 7 and ground in pin 8. Connecting the wrong mouse to a computer can fire it "some".
Commodore used a direct lecture protocol that charged the interpretation of the data over the processor.
On the other side MSX used an intelligent protocol that discharges the hard work on a little processor (MB88201) inside the mouse that sends the data over a 4 bit parallel port formed with the four direction switches. It needs four lectures of the port to form two bytes, x and y displacements on twos complements. Then the program managing the mouse only have to add the displacement to the actual position of the pointer to know the next move.
That simplicity of the protocol and its connection made it easy to implement it on other computers.
PC mice, both RS232 or PS/2 use a similar way to transmit data, but they do it over a serial line.
The mouse has two buttons. The ball and a light barrier with encoders are needed for the movement of the pointer's mouse.