Not to be overly picky, but there was no other "pure" VF-3 section - that is where both pilots were actually from VF-3 as opposed to one or the other or both coming from VF-42 - from which Thach could have possibly drawn a beam defense trained section.
In Thach's first division, he and his wingman Dibb were familiar with the tactic. I believe his third section, Cheek and Sheedy were familiar though to a lesser degree, Cheek was checked out for sure, but Sheedy had not long been in VF-3 so how much practice he may have had is problematical. I'd note in their action (Cheek and Sheedy, that is) they were operating as an unsupported section and did not themselves employ the beam defense when attacked. Thach's second section, Macomber and Bassett, were both from VF-42 and had not been exposed to, much less practiced in, the beam defense concept.
Those who flew fighters of Yorktown at Midway, Thach included, were very clear in that there was no familiarization, even on paper, with his beam defense on the trip out. The VF-42 pilots, in particular, had absolutely no training or any other familiarization with the beam defense.
There was only one other section in the whole squadron - third section of third division - which even had a section leader from VF-3 (Barnes with VF-42's Tootle as wing). Thach, himself, was the only VF-3 division leader; the other three division leaders were from VF-42. Of the 12 sections within the squadron's four divisions, 9 had section leaders from VF-42.
Thus, 33% of the VF-3 pilots flying in the battle were VF-3 and 67% VF-42. 75% of Division leaders and 75% of section leaders were VF-42. But, despite the preponderance of VF-42 pilots, generally, and specifically in leadership positions (not surprising as VF-42 was the most combat experienced VF squadron in the fleet) the squadron was VF-3 and commanded by Thach.
Also, what happened in terms of the make up of TBD escort was that Thach wanted to augment his 1st Division with an additional section from one of the other three . . . it was the Buckmaster, Arnold, Armstrong, and Pedersen planning group who scotched that idea, not Fletcher.
Regards
R