That would work, but if thats not allowed.

My KVM idea wouldn't be the best, but it would work.

Person X and Y, with their computers, X and Y, and the third computer Z.

At computer X and Y there is a two way KVM (so two KVMs) which has their own terminal and leads going into computer Z. Would require two moniter out on Z as well as 4 USB ports (2 keyboard and 2 mice)

Would basically mean that person X and Y just hit the switch on the KVM at their terminal when they needed to control computer Z or their own. Roundabout but software free way of doing it.