I have this problem. My settlers don't seem to want to man the weapons trading posts I built in Sanctuary or Castle. They man the junk trading posts with no problem So I'm sure I know how to assign them properly. It's seems to be just the weapons trading post.
I'm not sure about the other types of trading posts since I have not built any of them.
I think people have mentioned a problem with the level 3 trading shops...but the level 4 ones work fine.
I have done so, Headpopper. Multiple times. Even dressed one in a unique outfit so I could be sure I was issuing the command to the correct settler.