I play it (and most other first person games) with mouse-look/head tracking, using FreePIE. It's a bit fiddly getting it set up, but it should work with eye-tracking, too.
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First of all, love this game.
Secondly, it consistently crashes when I try opening the oven. I think there's an issue with my hands getting caught on the handle, or clipping inside the oven, or some such.
Thirdly, sometimes I rotate to the left when trying to sidestep. It doesn't seem to be something I can easily replicate, but it does happen. It's possible it's my 'body' getting caught on something, but it doesn't happen consistently, so I'm not sure.
Anyway, it's a fantastic game with a lot of potential. Keep up the good work!