A watch is… tiny! How were you able to smell it?
The Inspector was sweating and the watch case was metal. That doesn't hold scent well.
On metal, the volatiles boil off very rapidly. It makes for a strong scent for a very short time. If the watch had been here a day or two, I wouldn't have noticed it.
Florence puts out a lot of fluff when she talks. Things like safety, flight plans, life support. But every now and then she says something I really need to know.