Shape-wise, this looks a lot like a Hall's Hair Renewer.
If it had some embossing on it, this would be a home run. With no embossing, it is hard to say - perhaps $50 or so, but ideally I would want see much clearer photos or hold it in my hand to get a better sense for the age of the bottle.
I am simply unaware of brilliant ruby red glass in 19th century bottles - you do see earlier 20th century bottles (and some 19th century glass) so this is a real oddity.
Yes, gold is used to create the red color.