The first time a keyboard is recognized, it receives an ID number from the
computer and retains this ID number. When the multiple computers started
up, one after the other, they would all get the same Keyboard ID. The
problem is that when the keyboard is subsequently addressed, it assumes it
is communicating with just one computer and forgets its ID number. So
when a second computer attempts to communicate with it, nothing happens.
Conceivably, you could implement a program that echoed all the keyboard
information out from one "master" Macintosh II, over AppleTalk, but still
you would have to rewrite quite a bit of lower level code.