Sinclair did make a 12 inch Oils sign, see picture below;
They also made a 6 inch like this. The small ones that have the red letters on ebay like shown in the link below are all fake to the best of my knowlege. They did have red letters on some of the bigger ones
http://www.ebay.com/itm/SINCLAIR-OILS-OilGas-Porcelain-Advertising-sign-/190839438966The book "Oil Company Signs, a collectors Guide" by Benjamin and Henderson is a good book. It has a lot of good info in it but be advised, it does not show every sign ever used. I recently bought a nice old 1930's era sign at the Columbia Missouri show that while it was in the book, it was not listed as the same size as the one I bought. Either a mistake or there was more than one size of sign like it used back in the day. I reccommend the book highly.