JD-EE
When flying, you are typically looking at a variety of things that inlcudes looking at dials and instruments. It is not an either-or choice, it is "you must do both" and you don't get to choose not to.
The "look at it" is a subset of the required activity, true multitasking, particularly when flying in a condition other than straight and level flight.
Things breaking or behaving in unexptected ways just adds more
multi to the
tasking. (Apropos dealing with upset, and thus 447, task saturation is a critical point to understand in both training scenario design, and in task prioritization when things go wrong. I'll leave to psychologists and others the deeper details on why the human brain funcitons like that).
The analogy you used probably wasn't well chosen. (EDIT: OK, you updated it, I blundered on anyway ... )
It reminds me of what I used to tell ship driving colleagues about fuel when I flew helicopters from their ships.
"If your ship runs out of fuel, you will still float."
"If my helicopter runs out of fuel, it will first fall to the sea, and then not only not float, but turn upside down and begin to sink."
Their problem was in two dimensions, mine in three.
Maybe your non-moving, non-flying machine analogy is missing a dimension for appliciability.
(Oh, dear, back to dimensional analysis and Engineering 101, are we?
)