Not necessarily "all" of the cars had them. This plate was added likely by the regional distributor usually to cars that most of us would've called "leftovers" and essentially "redated" the cars to the current model year when first titled and registered. On this particular example, the "STC 60" would indicate a car that was built later in the 1959 CALENDAR YEAR but either sat on a dealer's or distributor's lot -- or simply wasn't shipped from England -- until very late in 1959 or perhaps even early in 1960 and then sold and titled. Back then, model years weren't very tightly defined, especially not by Federal safety or emissions standards. Also, there was very little to distinguish a "1959" Triumph TR3A from a "1960" Triumph TR3A other than those little tiny details that we anoraks debate endlessly! :wink: So, since no one wanted to sell "last year's" product as new, this sort of "retitling" was allowed.
All these years later, surviving cars have moved all around the country (and the world), so these tags show up on cars all over. I don't know if it was limited to Cal Sales and its successors as Western US regional distributors, or if other regional distributors did the same.
Meanwhile, nice TSOA badge. But is it NOS or a replica? Most originals would've had "Made in England" on the face of the base where the mounting holes are, and I believe you will also find "J Fray" and/or other OEM marks on the back side of originals. I've not seen any replicas close up, so I don't know how "convincing" they are in terms of such marks.