For me, sensitive horses don't really need to be taught how to half halt but can take time to understand to not overreact and to stay in rhythm.
I find slightly more onward bound horses, you might need to make the half halts a little bigger and more deliberate to help the horse to wait and really understand the hindlegs coming under and the shoulder lifting. You can almost feel the cogs turning!
I think you almost do it subconsciously, particularly in trot and canter, when coming up to corners, before transitions etc. rather than specifically having a session on teaching half halt.
Right from the start, same aids, but in a young horse it would be more to rebalance a loss of balance than to create more engagement. I've never really thought about it as teaching it, I just do it.