Heh, the thing about flaming eyes is they’re the one monster that “cheats” with respect to LOS, if they can’t see you, it just makes them fire the eyebeam and MAKE LOS. Turns out they’ll even do it underground, into the starting shelter basement, that was a quick game…
If a hulk or jabberwock can’t see, smell, or hear you, they’ll stay inactive.
Full list is hulk, grabboid, jabberwock, [REDACTED], [REDACTED] and tankbot. Technically the eye doesn’t have it, but its special ability does. Grabboids aren’t much of a big deal since they can’t leave soil tiles.