The opening of Winnersh Triangle station was reported locally on 17th May 1886 as "this week". So Monday 12th that year, as given in that leaflet, seems to be right.
The Gatwick service from Reading started in 1980, apparently near the beginning of May. I have not found a specific announcement, but BR added a mention of this to adverts they were already running for Railair Link. The first such mention I found in the British Newspaper Archive was on 7th May (in the
Wolverhampton Express and Star!).
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The name "Railair Link" was being used then more widely than it was later on, perhaps associated with the use of the name "Link Line" as on the leaflet.