zaidy78: That ma’ase is a bit hard to swallow. The Gra davened Nusach Polin (except in instances mentioned by his talmidim where he was cholek on the ‘popular’ nusach). The earlier siddurim of Nusach Polin have “Sim Shalom” written in for Shabbos Mincha, while later Nusach Polin siddurim seemed to switch to “Shalom Rav”. As a result it’s not clear what the Gra did, but it’s entirely possible he himself said Sim Shalom. The minhag in E”Y to say Sim Shalom by mincha on Shabbos in this case is from the influence of the Sefardim.
Outside of that, based on ???? ??? ???? ? and the Biur Ha’Gra there, it looks like he sides with the Mechaber (that one would be chozer also on morid ha’tal).
Though I haven’t seen it myself as I don’t think I’d begin to understand the sefer and as a result don’t own a copy, the siddur Ezor Eliyahu (Ashkenaz Al Pi Ha’Gra) mentions that based on the Biur Ha’Gra to Sefer Yetzira (?”? ?”?) it looks like the Gra would say “Mashiv haruach u’morid ha’tal”.
The minhag in E”Y is based on the Sefardim and Chassidim. That “mashiv ha’ruach” isn’t mentioned seemingly is in line with the fact that Sefardim don’t mention “mashiv ha’ruach” in their tefilas tal, whereas by Ashkenaz it appears as “Sho’ata hu mashiv ha’ruach u’morid ha’tal”