A Y splitter would only be effective when each item is powered one at a time, so there is only one digital stream at a time. Even unpowered the second connection to a device could terminate the signal enough to stop the whole thing. and it usually does.
It is possible to use a DVI splitter to get 2 poor adapted analog VGAs out, but even that isn't correct.
What is the purpose of a (simple) Y splitter? there really isn't one in most of the situations. Splitting to send a data stream to 2 monitors fails most of the time, feeding 2 computers into one monitor fails most of the time (including the items being off). The one use for them can be getting the Dual Link signal to 2 monitors. Everything else you need either a switch, or a distribution capability (splitter/booster).
What do people do when they buy one and use it? They have One connection that can Stay, and they move the wire off of either the second monitor, or off the computer (in your case) manually. Hey half done is better than undone right :-). They basically manually "switch" the cables, so why didn't they purchace a switch?
2 types of switches the Manuel A-B switch, very similar to the old parellel port switch no curcuits , just a multipole switch , that changes the direction of the signal without curcuits. Automatic switches with detection curcuitry. They come as single switch items, or in KVM (keyboard Video Monitor) switches. I would go for a well built manuel A-B or KVM hard switch, that had a good solid clunk to the switching.