There were (at least) two different types of Girling 10" rear brakes used on TR3/A (plus of course some of the Lockheed rear brakes were also 10"). The later Girling 10" brakes (before they switched to 9") did have adjustable posts like Don's brakes; rather than the hold-down 'nails' like the earlier 10" Girling and the 9" Girling.
The SPC gives the change point to the post as 15332; and TS13571L does have the earlier type with the hold-down nail & spring.
But of course the backplates do interchange, as do complete axle assemblies, so it's not at all unusual to find the "wrong" parts on any given car. TS39781LO had 9" Girling brakes when it came to me; likely because the entire rear axle had been changed. It also had a speedo for 4.1 gears, but 3.7 in the axle.
Those support posts can lead to an interesting problem; took me many months to figure out what that funny "clunk" was when I started to take off from a stop. (On a previous TR3A with the post, somewhere in the TS40xxx range.)