If you describe him or her "by contradiction" and using "not"-particle (e.g. "not_bad"), so the partner is "a".
"Well, he's good, of course", "she dances quite well", "his embrace is pretty good" – these are the obvious signs of "a"-partner. "The'-partners are usually described with a very special intonation. It's like aт exclamation of admiration "He is SOOOOOOOOO…….", and you immediately understand everything.
Of course, the most interesting is the question "How do I understand that the partner is "the"?"
Well, I remember a beautiful quote for this situation: "there are only two of us left, her, me and my bulging eyes."
Of course usually I understand that the partner is "the" before the moment my eyes become like that. The question is, how? What do I pay attention to, what is important to me?
I've been thinking about it a while and now I realize that two circumstances should coincide to make such a conclusion. First, I should feel comfortable with this partner in general. Second, this person must have some unusual quality that attracts me.
Speaking about the first point, I have pretty low expectations of the partner's technic. This allows me to dance without any problems with a wide range of partners. So this point is important when I don't find any attractive special quality or characteristic in my partner except dancing. Sometimes I am not interested in another person at all, sometimes I don't like his or her perfume or clothes, or how he or she dances with someone else. Sometimes I don't like that the person drinks alcohol or smokes or curses like a sailor.
Yes, in fact, there are many reasons for us not to like the other person.
If nothing makes me dislike a concrete person and I feel comfortable, then there is a second point, some unusual quality attracting me.
It may have nothing to do with dancing at all. Usually I am attracted by something like nice smell of her hair, special embrace, her breath or glance, micromotions of her body or her smile which I can feel with my cheek while dancing. Or it may be long and heavy earrings, or her casual dress without underwear. Her gently looking at me. Slightly opened lips. Smile, felt by the cheek.
It might seem funny to choose the partner by the way she pokes her smile on your cheek, of course. But it is as it is.