The pump part of the oiler looks like a Best and Lloyd pump. You find them on early motorcycles, or the application I am more familiar with, Morgan three wheelers. On the Morgan the pump would be dash mounted with one, or sometimes two sight glasses attached. You push the plunger in to charge the pump, it then returns slowly under spring pressure, the rate determined by the needle valve on the top of the sight glass. When you park up, the latch on the top of the pump locks it in position stopping it delivering until you are ready to go.
The Best and Lloyd pumps were marked with what is known as a “happy man” symbol on top of the plunger. In fact the little man is surprised rather than happy. This is a reference to the surprise gas chandelier which was made by the Best and Lloyd company.
Unless the pump has a specific and precious purpose, I would be inclined to remove the pump, fit a sight glass and get it onto a 2 speeder Morgan dash board.
Ian