This was the product of J. W. Nelson from Lexington, KY. I found at least one reference to a George H. Nelson, representing the company. He was probably the son. Bottle Picture courtesy of Daniel Lakatos.
Rectangular, about 7 3/4", flared lip, front panel, BIM, clear, horizontal on front: "NELSON'S - HAWIIAN - HAIR ELIXIR - MANF'D BY - J.W. NELSON - LEXINGTON, KY - USA"