Unless you are training the parents and then the offspring and then that offspring’s offspring.
Then you realize if what you are breeding for, those specific temperament traits, are there or not and why.
Folks, that is what purpose breeding is, why we breed known to known.
Of course you can see down the lines similar traits, is what we breed for.
Take for example, all equally talented, Gunner bred offspring in reining.
They will most be amenable, easy to train horses.
That is what they should bring to the table and that is what you find.
Even if you don’t know what the breeding is, when you train some of them, you can guess that is what their breeding is by how they present.
Other lines, well, you may end with the more difficult to train and motivate individuals, some more hyperalert and harder to focus ones.
Those temperament traits also predicted by their breeding and crosses from known lines.
The same for every other discipline out there with decades of breeding, training and performance behind it.
Yes, temperament is not a single gene, but it still follows known lines.