Well, this is a nice detective puzzle.
First clue: the article referenced in OP tells us that:
cajoling is difficult to distinguish from other types of behavior
that are unrelated to oestrus (e.g., sniffing for fresh air in the air
Next step: Google search for
veterinary cajole sniff.
On page 5 of the results, we find another article where the same table we saw in the original article is reproduced - with one difference: the word cajoling is now followed by an explanatory term in parentheses:
So now we know that cajoling is flehmen - and flehmen has not only a dictionary entry:
flehmen - a mammalian behavior (as of horses or cats) in which the animal
inhales with the mouth open and upper lip curled to facilitate
exposure of the vomeronasal organ to a scent or pheromone
which agrees nicely with our first clue, but also a Wikipedia article that teaches us that:
The flehmen response (/ˈfleɪmən/; German: [ˈfleːmən]), also called
the flehmen position, flehmen reaction, flehming, or
flehmening, is a behavior in which an animal curls back its upper lip exposing its front teeth, inhales with the nostrils usually closed
and then often holds this position for several seconds.
El flehmen es difícil de distinguir de otros tipos de conductas que no
están relacionados al estro, como la inhalación de aire fresco del
medio por lo que puede ser considerado de menor importancia para
determinar si una vaca está en celo o no (Van Eerdenburg y col 1996).