The T206 images of Dahlen were created from a Carl Horner studio image, which is shown below.
Dahlen was wearing a 'BROOKLYN' jersey for the photo shoot, as shown in the photo he's holding (below, right). This must have been taken during his first stint with Brooklyn (1899-1903), then modified to remove 'BROOKLYN', replacing those letters with 'NY', to reflect the team he played for from 1904-1907. By the time his first T206 card was designed, he was playing with Boston (NL) - 1908-09. He was back with Brooklyn for the remainder of his career (1910-11), as reflected in his re-designed 'Brooklyn' portrait T206.
The following is from Scot Reader's Inside T206, and is the most definitive explanation I can find for the scarcity of the 'Dahlen Brooklyn' variation:
As a side note, I've seen these cabinet images changed to reflect new teams, using two separate techniques:
1) Altering the negative, then developing a new print. I think that's what was done here to remove 'BROOKLYN' (just dabbing bits of black ink on the negative). The 'NY' was probably painted onto a resulting print. The same negative could be used over and over, as he changed teams. It looks sort of ugly on the cabinet you are looking at, but if it was used to create a mass-produced image (like a Sporting Life cabinet), the remnants of 'BROOKLYN' wouldn't be so obvious.
2) Doing all alterations on a print. There was one recently sold on the Net54 board where the old team name was 'whited out' on an actual albumen image (It was a St. Louis player, but I don't remember who). The Sporting Life cabinet image was then created directly from the cabinet. I saw it at a card show shortly after the original cabinet was sold here.
By altering the negative to remove 'BROOKLYN', Horner obviously no longer had a negative to create Brooklyn Dahlen images, making the one that Dahlen is holding in the photo below at right, that much more rare.
Carl Horner Studio cabinet
Bill Dahlen in later years, examining cabinet photos from his playing days. Note that the cabinet photo in his left hand is of the unadulterated 'Brooklyn' image.
Bill Dahlen and Kid Elberfeld appear in the 350-only group with teams they joined after the 1909 season. In particular, Elberfeld was purchased by Washington from the New York Highlanders on December 14, 1909, while Dahlen left the Boston Rustlers to become the Brooklyn skipper at sometime in the off-season between 1909 and 1910.
A timeline consistent with these seemingly incongruous data points would have the 350-only subjects created over a period of several months starting in the summer of 1909, with a few selective modifications to the artwork perhaps continuing into the winter of 1910. In accordance with these creation dates and known T206 availability patterns, general release of the 350-only group may have occurred during the winter of 1910, without Dahlen (Brooklyn) and Elberfeld (Washington). Such a release date would be consistent with known availability patterns since Barbeau (which was likely drawn in the fall of 1909, shortly after his team switch) is as ubiquitous as most other 350-only subjects, whereas Dahlen (Brooklyn) and Elberfeld (Washington) (which were likely created in winter 1910, after their respective team switches) are noticeably scarcer.