Conjoined Twins

I've wondered sometimes what exactly would happen if two conjoined twins were joined at their skull, and shared at least some part of their brain. Would they know what the other is thinking? Could this solve one version of the problem of other minds? Would this represent a case of true empathy? Would they be able to experience things from the other's point of view? Would you end up with three identities: one for each twin and one that synthesized both? If one of them closed his eyes, would he be able to have visual mental representations based on what the other is seeing? What exactly would the physical connection of the brains produce in terms of mental, psychological, cognitive and emotive states?

Well, at least based on the following short clip, it seems that my speculation was wrong, and that two twins sharing part of their brain are separate and independent agents, but it still makes you wonder what is going on in that area that's being shared, and whether the possibilities I listed above could ever obtain, doesn't it?

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