Closing your eyes is always an option, if you're trying to think deeply and without distraction. It helps a lot to explain your stream of consciousness as you think, even if it's disorganized, and you're definitely not cheating if your eyes are closed!
That sounds worth trying. And it would definitely be something to practice in advance...
When I've been aware of some of my hard-focused thinking behavior (am not autistic, AFAIK), sometimes I found I automatically tend to look away, at slightly interesting things (e.g., lines at the edge of a door or wall outlet, or some simple physical mechanism), and then sometimes it seems like 1% of my cycles are contemplating that. While the rest seems to be reasoning in all sorts of ways about the immediate problem and related things.
(In an interview, this is balanced with my awareness of the interviewer's mental model, and also thinking about the job opportunity that's the real point of the exercise.)
I don't understand how that works, but it usually works very well for problem-solving outside of interviews.
If I tried to switch up that automatic process, by closing eyes, I don't know whether the habit of visually contemplating something in parallel is a Chesterson's Fence, and then the magic wouldn't work.
Though, would be funny, if you were in an interview, trying this eye-closing tactic for a hard-thinking problem for the first time, just so you wouldn't look like a cheater, and you find this puts you in some other mental mode. Combat Mode, for example, where maybe you're suddenly finishing the interviewer's sentences, disregarding things they say you think are irrelevant, redirecting and cutting to the chase, with a calm but energized and commanding manner. You might get permabanned from that company, for coming across like an aggressive jerk, but they started it by creating a jerky interview process. :)
