I cannot move a unit into a tile which displays a caravan directly, however I can move a unit into a tile which contains a caravan if I am moving past the caravan and run out of moves.

When my unit is on a caravan, I cannot move it out of the tile. And, if I try various options involving trying to move the unit off the tile and trying to select the unit and so on, I lose the ability to move the unit even after the caravan has left. (Reloading the game at this point allows me to move the unit.)