To fix: Manually save (an extra save is good), quit the game, start the game, NOW use the compass button. Possibly just a relaod without exit will work but that is untested by me. Depends on if the issue is resolved by a fresh load or a software restart,

I see there's a lot of confusion with this out there. Some people get very close but they often land on incorrect ideas as solutions. It makes it worse that people may have the wrong button or just assume it is. Some of dealing with this puzzle here adds increased confusion when the game code is bugged, so its expected to land on incorrect conclusions.

Edit: Looking at other problems people have, it may also randomly affect other parts of the game. Someone else did post elsewhere about this stuff working with a different problem.

I had a bug just trying to get to the Stoneship age because rotating the tower wouldn't give me a red line pointing to the Planetarium. The other red lines showed up fine. I double checked to make sure the switch was on, tried resetting it a few times, and even tried turning off every switch except the Planetarium but nope, that red line just wouldn't show up. Had to look up the info so I could keep playing.

edit - I see you're playing the 2021 version but I'm playing the Masterpiece edition. My goof. Did you have any problems getting the red line to show up on the map? Maybe they fixed it and I'll give that version a go instead.

The rotation line worked great for me in Myst 2021. Its very snappy and visible. Snaps to each location very well. But, the version has its own other bugs, and the screen going blank for light switching from what I think I read is for "performance" reasons - that shouldn't ever be a thing (and should never have made it into a release build full stop halt the presses).

But, going forward, its the only version I will play. Its otherwise more enjoyable today despite the bugs than the other versions.

If you go with 2021, hope you enjoy it.