Thematically it makes sense that a player can move them around without the opponent necessarily knowing what they are.
I can imagine debating it in both directions from a theme point of view...
But it makes no sense from a rule point of view. At least I don't recall any rule which made me think you can move sighting markers. Note that you move units. Sighting markers are markers.
(But it's been too long since I've played. Do you have some relevant rule in mind which I may not be remembering?)