I do not give them the chance to stop and look at whatever they're spooking at. I know both ways probably work, but I believe that allowing them to stand and star and gawk at something for 5 minutes is reconfirming that this is something worth being worried about, because the rider has stopped and is looking too. Also patting and soothing - what does a stallion do in a herd? Does he stroll over and stroke and comfort mares that are worried about something, or does he turn around and give her a bite and tell her to get moving and get over it?
My horses, whether babies or schoolmasters, are made to work past the scary object. Basically I just entirely ignore it. If the horse leaps sideways, I'll spin them the opposite way to which they leapt, and then ride on. Next time I ride past it, I will flex a little to the inside and push them across with my inside leg. I don't look at whatever they're spooking at, just ignore and tell the horse to get over it. This way they learn that it's not worth worrying about, if the rider/boss doesn't care, neither should they!