At the almost certain risk of getting shot down in flames here, regarding formation lengths on the HSTs, strictly speaking, (depending on your location on the ECML) any rake from 7-9 would be accurate if you think of the likes of, say Services to the West country which were 7 coaches - not an East Coast set, but a 7 coach formation on the ECML
Now - as for rakes of 9 coaches. I clearly remember reading one of my Grandfathers' Railway mags back in about 1980/1/2 which had a photo by (I am sure) Brian Morrison showing an HST somewhere in Fife or thereabouts either going to or from Aberdeen.
This had a 9 coach set (which I counted) - I can't be more specific than to say 1980-81 was the time frame I saw this pic (which was black and white, the mag might have been older than that).
So an odd 9 coach set on the ECML?
Well, unless I am totally wrong, this set had a "255 XXX" set number on the nose (the shot was taken, presumably from a bridge, angle showed number on nose, but was a fairly head on shot)
Why do I remember this? Well, when I saw the number I thought "Hold on East coast 125s are 254 numbers." I found another few shots in other magazines and first was a western set (253) and I noticed that had 7 coaches - then and East coast set (254) which I noted had 8 coaches - it was THEN I counted the coaches on the shot in question and there were 9 - I personally assumed "So, 253=7 coaches, 254=8 and 255=9 coaches"
At the time I was about 10 years of age and apart from being fascinated by 125s, formations and numbers of coaches were something I knew nothing about and the 253/254 system meant nothing to me, except that every set I saw on the ECML was 254.
Now, I have never found proof of this since, and apparently 255 was later (or 'only') allocated to the shorter Virgin HSTs but not carried, but as I say, I can still remember this photo to this day - either I am totally wrong....
I can't seem to post Links to the group, but if anyone looks for "Weirs Way Berwick" on YT, skip to 22m 20s and theres a 7 coach HST heading north over the Tweed.
Similarly (and to confuse things) Bill Watsons' "Iron Road" Smugmug - '1980s monochrome' shows a diverted 9 coach HST set (254 on the nose) in 1980 in the Pelaw area I think