Making J/P refer to extraverted function rather than dominant function really came in handy for identifying temperament (both conative, and the Interaction Styles as well) in the types.
http://player2000gi.host-ed.net/jungian_functions.htm, that defines T as linear and F as holistic (and I had assumed drew from her because it mentions the brain hemispheres as well). She did not agree, and couldn't seem to understand the rationale behind that, and I was having trouble explaining it, but it did make sense (you have to see his illustrations on the page to get an idea).
So if both are true, it means that T and J are both linear, but perhaps in different ways, while F and P are both holistic.
I know in Bruzon's theory, linear/holistic are connected with the "connections" between events (T="this causes that" with lines connecting the dots; F is more about an overall "harmony" represented by events being enclosed in a circle).
To Lenore, linear/holistic is
J[Je/Pi: left brain]="one-after-the-other" rules; desires predictability; structuring reality before it exists
P[Pe/Ji: right brain]="all-at-once" approach to life; desires probability; adjusting to conditions here and now, in light of their impact on our goals.
So these sound similar, but both can be true.
In my correlations of type with the old temperament systems, using "people/task focus" as the other factor besides introversion/extroversion; I discovered that T and J are both "task" focused" (less "responsive"), and F and P are more "people" focused (more responsive). Task-focus is "directive" for the Interaction Style (S+T, N+J) and "structure focused" for the temperament (S+J, N+T), and people-focus is "informing' for the Interaction Style (S+F, N+P), and "motive focused" for the temperament (S+P, N+F).
So what's happening is that linear and holistic seems to be connected directly to task vs people. But in two different areas. What we end up with is that TJ's are the most linear; FP's are the most holistic, and TP's and FJ's are inbetween; mixing linear and holistic in one way or another.
(Would this seem to fit those groups in anyone else's view?)
Bruzon's use of the terms are connected with tying together our perceptions, and Lenore's seem to be more about the actual decision making process itself.
In Bruzon's theory, it is the perceiving function that determines the orientation, which he frames as the "matrix". Pe=wide area matrix, and Ji will operate off of this. Pi=local area matrix, and Je will work off of this.