Wandering traders do not wander on their own. They do wander/run if they are being attacked by zombies, illagers or players. They only stand in one position while their llamas push them.
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[Mojang] Mega_Spud (Jay)
migrated
I think this is actually the same issue as MCPE-45756 - I'll update the title to make it clearer. Feel free to add in a vote and a comment to MCPE-45756 if you would like.