Atari released its ST home computers. This mouse probably was designed for that.
Labeled:
ATARI STM1 ATARI CORP MADE IN TAIWAN SERIAL NUMBER A1 5010799
According to Wikipedia, "The Amiga and the Atari ST use an Atari standard DE-9 connector for mice, the same connector that is used for joysticks on the same computers and numerous 8-bit systems, such as the Commodore 64 and the Atari 2600. However, the signals used for mice are different from those used for joysticks. As a result, plugging a mouse into a joystick port causes the "joystick" to continuously move in some direction, even if the mouse stays still, whereas plugging a joystick into a mouse port causes the "mouse" to only be able to move a single pixel in each direction."
Presumably the Atari mouse knows how to behave on a joystick port.