The PS2's dedicated mouse port follows the PC industry standard: purple. The keyboard port is green. This color coding dates back to the original PS/2 connector spec (hence the name) and carried over to the PlayStation 2's USB-to-PS2 adapter dongles and the few native PS2 mice Sony licensed.
If you're looking at a PS2 console or adapter and see a purple PS/2 jack—that's for the mouse. Green is keyboard. Some third-party adapters skip the color coding, but purple/green is the official convention.