Q: Where is the mind? How does it multi-task?
A: The mind is where you put it to. E.g. If you think of your fingers typing, your mind is there then. Multi-tasking is an illusion. We can only do one thing mindfully at a time, though we can train to do many things quickly and some mindlessly (absent-mindedly) at the same time. E.g. It is possible to chew food mindlessly while reading a newspaper mindfully, but not possible to do both equally mindfully, as the mind can only be properly mindful of one subject at a time. So, when multi-tasking, one is actually doing A after B quickly or alternating between the two rapidly; never really A and B at the same time.
Enlightened beings, however, with complete mastery of their minds and supernormal powers, can manifest at many places at the same time do perform different tasks. Note though, that the Buddha taught us to train single-minded concentration in the meanwhile! E.g. the practice of mindfulness of Amitabha Buddha (Amituofo).