FYI popa_bar_abba Rosh Chodesh Sivon has absolutely nothing to do with timing of Shovu’os.
Shovu’os depends exclusively on timing of Rosh Chodesh Nisson, being 9 weeks & 1 day after Roch Chodesh Nisson; This being so, even in olden days, after 9 weeks everyone knew when Rosh Chodesh Nisson had transpired, which by default makes entire institution of Yom Tov Sheni by Shovu’os even wishier washier than by Pesach & Sukkos.