Some of the parameters for attention seem to include:
Speed and rhythm of attention shifts. Am I focusing solidly on one thing? Or am I switching back and forth between several things, like a student driver who must keep track of their feet and their hands and other cars and pedestrians and signals? When I am distracted, how reliably do I return to an intended object of attention? (I say “rhythm”, but “melody, meter, and rhyme” might be a better analogy.)
The ratios between attention on different sorts of targets: external (senses, objects in the world, people saying words at me), bodily (stuff my body is doing: motions, itches, weird inner ear noises, gait, hunger), and reflective (stuff my mind is doing: inner voice, memory recall, making plans, worrying about that weird inner ear noise).
The strength of episodic memory formation; and the subjective passage of time. Short-term memory is how we perceive time passing; people who are not forming short-term memories (e.g. alcoholic blackout, senile dementia, high psychedelic doses) don’t notice time passing, experience frequent deja vu, repeat the same “discovery” over and over, etc.; they may have extended attentional focus on a single object because they’re just having the same thought repeatedly without forming memories.