I can't see that the USB mouse cable has both PS2 and USB signals down the same wires and the convertor merely selects the PS2 signal wires to the PS2 port.

The convertor acts as a "dongle" to the USB mouse, and clues it in to start doing PS2 protocol down the wires instead of USB protocol (perhaps by having the voltage wires the other way round -- or perhaps simpler than that; isn't PS2 5V whereas USB is 12V?). The convertor will be specific to that USB mouse and is not a generic USB-to-PS2 convertor.

Peter