I really cant say that the defense of " I can't smell it" will fly, simply put is this.
If it has flavoring in it at all, then it has a smell, not saying this to be a downer but its something that I heard a while back and still drives me up a wall and down another which is "Ecigs have no smell"..Uhhh yes they do, depending on the flavoring a very strong one at that.
I'm not saying right or wrong, don't get me wrong here...I'm actually picking on no one as E-cigs smell a million times better then Analog tobacco cigs any day however the defense of "I can't smell it" won't fly. And your not crazy you may have just gotten used to it. I'm reminded of folks that live with cats that don't clean the litter boxes on a regular basis (or even if they do) their house has a particular smell of...well cat. Same with folks that own dogs and the like, if you ask them if they smell the house then they will normally say "I smell nothing" but that is because they got used to it. Your not crazy just experiencing being human is all
I'd say go on and explain what an ecig is, show your landlord the equipment and how it works. There are plenty of information places including ECF you could direct him/her to for questions to be answered in detail. Worse case is if they are not ok with it you may have to step outside to vape. I will say that a bath or dish towel will catch the vapor very well on exhale to include the scent if you have to stealth vape as I've done that at work once or twice working doubles on night shift myself (I used a small Kleenex sized towel for those times at work, did the trick no problem).