Vladas, I'm sure you already know this. But for those that don't. Whether talking about a bedded coyote or Red Fox.
Neither canine spend any amount of time looking up-wind. "After they've been bedded down for awhile". Especially, the Reds. Which makes them much easier to stalk in on. Than that of the typical bedded joe coyote.
Only time either canine will look up wind is "if or when" they hear or scent something that peaks their interest to their up-wind. Otherwise, a coyote that is a nomad or a neighboring coyote that is tresspassing. Will "often" pan around 360.
Regardless of wind direction. I personally believe this behavior(looking 360). Is, because they know they are tresspassing & on the look out for the locals.
Regardless, I prefer to stalk in on a bedded canine from their angled up-wind. Unless they look my way or happen to hear me stalk near. I'm out of their line of sight & they can not scent me.
Another behavioral difference between a coyote & a Red. Is the Reds most often dismiss ambiant noises a hunter may make. Which often is their down fall as a hunter draws near for a shot.