Sniffing can be a displacement activity. Sometimes when dogs are nervous (eg, when another dog is nearby) or a little uncomfortable they will put there nose down and delibrately sniff. It's not a proper sniff and I think it looks a bit different to a proper sniff.
I have seen Holly do a displacement sniff (and she is a very sniffy dog, when off lead at the park she spends about 75% of her time sniffing and the other 25% running, she loves smells and loves doing scent clothes for obedience). When she does a displacement sniff she sort of moves differently and it's a lot faster than a proper sniff and more erratic (even the way she walk/runs is different). It's hard to explain but it is very different to when she is actually properly smelling something.
So perhaps that has something to do with it. Maybe Brody wants to be near the person but at the same time he is uncomfortable so he is sort of using sniffing as an excuse. as a displacement activity?
Only you know how he is sniffing and how he interacts with people so I guess you need to judge why he is doing it yourself. But I think it would be beneficial to try and identify
why he is doing it rather than just trying to stop it.
If it is a displacement activity then it might resolve itself in time. I think dogs do go through waves of different behaviours as they get used to their new home (especially adult rescue dogs). Someone once told me that around 6 months after getting a rescue they will go through an "odd" phase where they can become very difficult and display new behaviours, I'm not sure if it's true and I can't remember how long you have had Brody for.
If you really don't like the sniffing then the only thing I can really think of to do is to redirect him, when you want him to stop get a toy out and invite him to play with that instead.
Anyway, whatever the reason for the sniffing, doing more controlled sniffing activities might not directly stop him sniffing (I'm not sure you can tire out a dogs nose or desire to sniff). But it could definitly help him if it gets his brain going, increases his confidence and gives him an outlet for his energy.
So, some ideas are:
- If he has a favourite toy you could teach him to find it. First put it out in the open and tell him to "find it" (or whatever cue you like) and praise him (play, treat, whatever) when he grabs it, then slowly start to hide it, increase the difficulty (hide it with him out of the room).
- Hide treats around the room, this is similar to throwing them on the lawn but you put them around the room for him to sniff out (remember where you put them or use something that wont stink if it goes off).
- You could teach him to do proper "scent clothes" like an obedience dog. I could tell you how if your not sure how and want to do this.
- You could teach him tracking. You might need someone to help by laying the track (could do this at the park), but Brody could stay on lead for it and you could incorporate it into your walk (would probably only be able to do this once a day at most anyway). I've never done tracking so someone else might be better at explaining how to teach it.
Sorry for the long post, I hope it helps