Paul,
I’ve not used the Birchwood Brass blackening, but have used horological blackening fluid for many years on small model railway parts. The first thing is that all chemical reactions work faster the higher the temperature – 14C is far too cold! Although not directly related, I have used stainless steel blackening fluid where the instructions state it must only be used with a 23C air temperature.
For small parts, put your blackening fluid in a container of warm water to improve the reaction (and hopefully, the quality of the results). For finish, it depends on what you need. One mate uses “dewatering oil” (NOT WD40!!) to protect non-painted parts. I usually lacquer mine – Rustin’s Metal lacquer works well and is easy to apply.
Tom