Depends on the trainer but the ones I know/knew/dealt with didn’t really “shop” at a set time and place for a set period of time. More like they were always shopping listening to other trainers pitching a sale. Always selling too, always pitched anything they had clients trying to sell. What do you think those trainers are chatting about when you see them talking with each other at the shows?
There’s all kinds of trainers out there with all kinds of ways of operating. Just be sure you are clear on how the trainer you are trusting to act as your agent or evaluate a horse for you is going to charge you before getting involved. There is no one size that will fit all so never assume they will do it the same way as another trainer does.
Be sure they are worth trusting too. Many are not.