A highly controversial exploration of consiencesness can be found in
Penrose, R. (1994). Shadows of the Mind. Oxford University Press, 1st ed.
It argues conscienceness can't be modeled by a turing machine, using Godels theorem and then hypothesizes that quantum mechanic effects in microtubili inside neurons might play an important role in the emergence ...
One approach to this is to search for "habituation", "learned task", "concomitant task", "dual task" and "multiple task" studies, which may include cognitive and physical aspects (memory, reaction time and such). "Background tasks" are usually related to computers.