The Oxford Names Companion, OUP "Scottish Forenames" - Donald Whyte, FGH, FSG
Notes:
1. Gaelic form of Jane [q.v.] or Jean, feminine forms of John, Anglicized as Sheena. The Irish Gaelic form is accented: Síne. Sineag is a Scottish pet name.
2. Danish pet name for Latinate names ending -sine or -sina.
Thanks to Donald Whyte who provided much of the initial information for this site.