I believe that the "enigma" witnessed in some types is due to the disparity between personal vs impersonal factors in some of them.
Personal (relational): Feeling, informing, motive focus
Impersonal (task): Thinking, directing, structure focus
For the FP's and TJ's, all of these are in sync.
It is the TP's and FJ's where they do not all line up
STP Thinking, directing, motive focus
SFJ Feeling, informing, structure focus
NTP Thinking, informing, structure focus
NFJ Feeling, directing, motive focus
All Feeling types are informing except the NFJ's.
This is perhaps why they have taken on the biggest reputation of being "enigmatic".
Feeling is usually connected with the "responsive" people-focused social skills Keirsey dubbed "role-informative", yet this one pair of types still manages to be role-directive like most Thinking types.
Directive is more than just issuing directions, though they probably do that enough. Keirsey, in Portraits of Temperament identifies it as "defining the relationship". Basically, it's an attitude of "don't call me; I'll call you", as described for the corresponding "low Wanted Inclusion" in the FIRO and APS systems. It conveys more of a "criteria" for social responsiveness.
Hence, the types seem a bit aloof, distant, and perhaps unapproachable to most, even though they are still a Feeling type, and an extraverted Feeling at that. This (coupled with the misty introverted iNtuition that tends to make them directive in the first place).
All Judging types are structure focused except for NFJ's
Likewise, structure vs motive is sort of "directing/informing" on another level (conative action and leadership skills instead of social interaction skills), and Judging is usually structure focused (fitting people into structures such as organizations or plans), but this one pair of types manages to be motive focused (take into consideration "why people do what they do, in order to work with them"; this factor identified by Berens, connecting SP with NF and SJ with NT).
Hence, the types still have an inner warmth, inside of the intuition and outward spunk of directiveness.
So basically, NFJ's are task-focused where we would expect them to be more people focused; and people focused where would expect them to be task focused.
All Thinking types are directing except the NTP's.
These types are probably considered "enigmatic" as well, and a big part of that is probably the "informing" nature making them a bit softer than other Thinkers. The biggest result of this is many struggling with the T/F dichotomy and being confused with NFP.
All Perceiving types are motive focused except for NTP's
This also creates an interesting mixture, of the non-seriousness and openness of P with the seriousness and tough-mindedness of T.
So they too are task-focused where we would expect them to be more people focused; and people focused where would expect them to be task focused.
The S's don't get the tag of "enigmatic" (for fairly obvious reasons), but here's the disparity as it continues onto their side:
All Feeling types are motive focused except for SFJ's (hence, their much noted strictness)
All Thinking types are structure focused exept for STP's.
All Perceiving types are informative except for STP's.
All Judging types are directive except for SFJ's.