I at least look up toward the ceiling while thinking so maybe that’s sufficient to not give off cheating vibes.
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. :)
It’s actually fun how in video calls everybody thinks they’re doing eye contact by looking at other people’s faces on screen which in reality makes them look down and not straight at the camera.
The weird thing is, it looks like I’m looking at the off-screen when I’m actually watching the video, and vice verse.
To me, it's actually the lack of any indication that work is happening that gives of cheating vibes. If someone sits their glassy-eyed for twenty seconds, and then starts speaking in complete sentences, it is going to come across as though they are reading. Not to mention that people's intonation is often different if they aren't thinking up what to say.
If you do get stuck, you can avoid ambiguity by sharing some meta-commentary on what you are thinking and why. "I know that library uses X, but I'm not sure if it can do Y and I'm trying to think if I could work around that... okay, so what I would do is..." Something like that, so that the interviewer knows where your ideas are coming from.
But this was a case of someone staring at a specific place off-camera while "thinking" while their eyes very visibly went rapidly left and right for 20-30 seconds, and repeating the same thing for literally every question, even the ones that were intentional freebies based on their resume that they should have been able to instantly answer.