Keep in mind the light is never changing in direction or intensity, I'm not even sure there would be wind in any meaningful sense. There's be some, the world might be tidally locked but it isn't likely to be in a circular orbit with no eccentricity at all, so it would have 'seasons' even though the sun never set, and those would vary in keeping with that eccentricity. If it, say, was closest every year at 10 million miles and furthest at 20, it would receive 4 times as much light during the 'summer'. Air would warm up more and push out toward the dark side, probably most near the equator since it would still be a sphere with it's polar sections tilted and getting less light, even if it were perpetual. Then in the winter as the world cooled the air would contract and move in from the dark side. Moisture traveling would be higher in the hot, out-pushing summer from the extra heat and likely far lower on the winter 'night side wind' plus the moisture deposited on the dark side would freeze and the net effect would be to produce a dry day side and an equally dry massive glacier night side. The twilight regions would presumably get some thawing water run off in the summer and I wouldn't rule out enough moisture returning in the winter to day side to come back with the 'summer winds'.

That said I tend to be dubious about the notion of a habitable twilight ring around these sorts of worlds, I'm pretty sure it wouldn't be a ring anyway, more likely an interrupted ring minus the polar section or vice versa, or maybe even a ring with two wide sections near the poles. I'm not sure if anyone has actually sat down and really worked it out, since there are so many minor variables that require too many generalities to get specific on. Then again I'm notoriously pessimistic about colonizing planets, I tend to view them as worthless chunks of rock with too large of gravity wells to make mineral extraction worth it, even for the ones in our own solar system.