Wow, thank you so much @100th-Coin for playing and recording the session! It was very cool and instructive for me to watch. I completely agree that some mechanics were not explained very well. We're planning to do a post-jam version of the game with an additional level or two just to introduce the mechanic in a clearer way.
You are only ever able to interact with a lever if you're standing next to it, you were just very unlucky in that you pointed the mouse cursor at the lever at the exact moment the lever flipped because of the timer.
Also, the fact that you assumed you needed to walk over to the lever was part of the design of the puzzle. It was an intentional misdirection, also called "the Catch". If you're interested in puzzle design, I recommend you the following video from GMTK, especially the second part "the Catch": https://www.youtube.com/watch?v=zsjC6fa_YBg