^
I think that nearly all animals have a responsiveness variance to them that creates different personalities to them in a way that resembles extra/introversion in humans. And depending on the animal it can probably get a lot more complex than that. But some traits like sensing/intuition probably just don't exist much at all other animals. (Not that we know of anyway.... but I bet animals like dolphins, chimpanzees, and bonobos have some chance of having personality types in an almost-MBTI way but just more simplified. Too bad we can't know them yet because the types are on a self-reporting basis
)
Type is a combination of
behavioral and
cognitive factors. The behavioral breaks down into "affective" (interaction Styles) and "conative" (what we know as the Keirsey groups). Or, respectively, social and leadership/action skills.
So yes, animals can manifest the affective factors of expressiveness (i.e. E/I) and responsiveness (directing/informing or how much interaction we "want" from others), which make up what amounts to the four Interaction Styles.
These are what were observed by
Pavlov in the
four temperaments he assigned to dogs. He called the factors Passivity: (Active or Passive) and Extremeness: (Extreme or Moderate response) and the four temperaments as Weak inhibitory (Melancholic), Strong excitatory (Choleric), Lively (Sanguine), Calm, imperturbable (Phlegmatic).
It is the cognitive area animals do not have. The functions are basically
interpretations of data. Animals experience things, but do not cognitively
interpret them. They just
react according to the limbic system of instinct and emotion (basically, archetypes).
We experience things and also react from the limbic system, but in addition use the frontal cortex to interpret the limbic system's images freighted with emotion. The functions
translate this limbic motivation into cognitive data, allowing us to redirect the instinctual "energies" the limbic system mobilizes.
The way this works, is that we're faced with a situation. We take in data from what is happening. If it is a negative situation, then our instinctual reactions and emotions such as fear kick in, just like they do for animals. The difference is that the animals remain guided by the instincts.
Both have "sensation" of what is happening, but the human cortex interprets the data, and if the person's cognitive
preference is 'sensation' itself (S), then the person will focus more on what is seen, heard, felt, etc. and react to it based on these factors. (So animals
aren't even "Sensors" by that criteria!) If the preference is iNtuition (N), the person will instead connect the data to a larger meaning that is not immediately seen, such as the possible or likely outcomes.
If the person prefers Thinking, they will focus on the cause and effect of the impersonal elements of the situation, both in analyzing why it happened, as well as in deciding on courses of action. If the person prefers Feeling, they will focus on the more "humane" or personal aspects of the situation. How it affects people, especially emotionally. That any courses of action should take into consideration their needs and well being.
Animals do not do all of this, so they do not possess any of the dichotomy preferences beyond E and I. (Which is likely based on neurological stimulatability anyway, rather than being fixed to human "[dominant] function-attitudes". We just pair our dominant function with that dominant orientation, and the rest of the functions fall into place for us).
So they can be seen as having somewhat of an Interaction Style, with E/I, and the other factor; which for us is connected to T/F or J/P combined with S/N; but for them stands alone.
They will not have a whole type, or even a Keirseyan temperament. (Which are determined by functions, despite Keirsey's claim to the contrary). They won't even have the other Keirseyan factor of "cooperative/cooperative", or the cross factor of "structure/motive". So their "conation", "leadership style" or "area of Control" is undefinable. That stuff is part of what distinguishes us as humans.