This is a tricky question - and one to which I do not have a settled answer.
But in the classic research programme into interpersonal differences (which was pioneered by HJ Eysenck), personality is regarded as distinct from intelligence.
This means that ideally there should be no significant correlation between personality and intelligence, but when there is there should be possible significant dissociations - such that high levels of a specific personality trait should be found with both low and high intelligence, with the same applying to low levels of that specific personality trait.
How this works can be seen in a draft, in press book chapter on the evolution of Simon Baron-Cohen's concepts of Systemizing and Empathizing (my co-author is Patrick Rosenkranz):
Empathizing and Systemizing conceptualized as personality traits
Empathizing and Systemizing are conceptualized as personality traits, dispositions or preferences to behave in certain ways; therefore not as cognitive abilities.
E-S variations are thus not-necessarily correlated with cognitive abilities – and indeed in some studies there is no significant measurable correlation with cognitive abilities. For example, there is neither a strong nor consistent association between the ‘reading the mind in the eyes’ test (a test of a cognitive ability), and scores on a self-evaluation Empathizing scale (a measure of disposition or personality): so that an individual may score highly at reading the mind in the eyes but score low on an Empathizing scale, or vice versa (Lawrence, Shaw, Baker, Baron-Cohen, & David, 2004; Voracek & Dressler, 2006).
A disposition is a personality trait: understandable as a sustained tendency, an individual’s characteristic of habitually deploying a mode of cognition. A disposition can also be seen as an individual’s preference for using an ability. (In the sense that preferences can only select between a certain set of abilities; one cannot characteristically be disposed to act in any way that one is incapable of acting.).
And preference to behave in certain ways is (presumably) based on a motivation, and motivation is associated with a psychological reward (or gratification) from doing something – or else a psychological punishment (or aversive consequence) of not doing something. Ultimately, therefore, a disposition reflects that certain types of behaviour lead to increased gratification (increased pleasure or diminution of suffering). Individuals differ in the types of behaviour which lead to gratification, and in the degree of gratification associated with a specific type of behaviour.
In sum, individual and groups variations in Systemizing and Empathizing can be understood as variations in the type of behaviour that (on average) lead to gratification. Put simply, Empathizers gain enhanced gratification from Empathizing behaviour, while Systemizers gain enhanced gratification from Systemizing behaviour. For example, a High-Systemizer may have the ability to understand and empathize with other people, but prefers to spend most of his time doing crosswords; while a High-Empathizer may be able to do crosswords to a high standard, but she would prefer to converse with a group of friends.
Naturally, the disposition to be Empathizing or Systemizing requires that there be the cognitive ability to do these; to empathize requires the ability to empathize and to systemize requires that ability. And at extremes of disposition there may be a deficit in such abilities, so that the extreme Empathizer may be defective in systematizing ability and the extreme Systemizer may be defective in theory of mind ability.
However, deficiencies in either E or S ability are not necessary to the finding of variations in E-S, and it seems that there may be a wide range of E-S dispositions even when both abilities are fully intact. Therefore, these abilities must have evolved in order that there be a disposition to use them.
If intelligence and personality are regarded as autonomous; then this could be because personality is reducible to something like cognitive structure (maybe even to the formal properties of brain circuitry - the broad systematic principles upon which the brain is 'built')...
While intelligence could be reduced to something like processing speed - the efficiency (including rapidity) of cognitive processing - for instance as (crudely but objectively) measured by reaction times.
On this basis, how might personality be measurable, objectively?
It would ultimately be a matter of how the brain is setup - the principles on which it is organized.
The idea would be that different personalities would process information differently, according to different principles - and we are talking about qualitative differences, and specifically not about the rapidity of processing.
So, the same informational input would lead to different behavioural outputs, according to different personalities.
If this analysis is broadly correct, it can be seen why it has proved so much more difficult to measure and in particular to classify personality, than intelligence; since it does not seem obvious why there should be a fixed number of personality types except perhaps at broad categories of gene pools and in response to natural selection.
Much of personality difference would then be random variation, the results of many types of pathology, and the variation due to ongoing, unfinished 'selective sweeps' of natural selection - when past natural selection has produced personality change in a proportion of the population, but either this process is incomplete or else the direction of selection has changed.