Jack, I imagine that needle oiler has a pretty fine point on it? I’ve been using this little Nalgene dropper bottle for years. The tip could be finer (and longer), but it works well enough. (Shown here with several Lambsfoot knives I still had out on my table/workbench after a bit of recent maintenance.)
I refill it with mineral oil I bought at the pharmacy (labeled as “Intestinal Lubricant”).
That’s interesting. I don’t think the pharmacy mineral oil I use is particularly “fine,” but I’ve never had it gum up on me.
I like Ballistol. I mostly use it for firearms, but I’ve also found it helpful for knives that ended up with some rust on them. Seems to work better than mineral oil for removing rust (without having to resort to some sort of rust eraser or polish).