Teaching the horse shoulder in is important for them to learn to have even weight in the shoulders. Since we know this is critical for the horse to carry our weight comfortably, I start teaching this once the horse understands to follow the hand in longeing, scribe the circle and has had a lot of practice with the start and stop exercise. https://classicalequinesolutions.com/2021/10/04/in-hand-work-for-improved-communication-and-balance/

This is my young Lusitano stallion on his first day and then fourth day of learning this. He already had the idea to move away but not the idea to catch it and not just fall onto the other shoulder. I always start teaching this just the cavesson, using the bit is for a horse that understands the movement.