There's no reason to do so. The view requirements for the normal exterior mirrors do not cover anything inboard of a plane parallel to the vertical longitudinal median plane and through the extreme outer point of the vehicle (vehicle/trailer combination). There's obviously nothing stopping you installing something that allows you to see inboard of that plane and possibly revealing your trailer but I don't see anything that forces you to do so. There's a limit to how far your mirror can project outboard beyond the widest point too, which might scupper the idea for your trailer anyway.
Look more closely at your standard mirrors. The markings are not on the glass, they're moulded into the plastic housing. LR have been using class III mirrors since at least the late RRCs - you'll have them, too.
Hit the brakes very hard - they'll soon learn that they can't be seen! Did that once in the fog with a 'Roller' that wanted to be in the back of my ex-mil Series IIa (bumperettes, NATO hook etc.) - very effective it was, too.