Lubing a jeweled pivot like that, is like lubing a watch. A drop is about eight times the volume needed.
We use oilers, which are basically fine wire with a "spoon" shape a few thousandths wide on the end. Different sizes depending on which pivot is getting which oil (and there are usually about six different lubricants used in a mechanical watch).
You can get some CRC "Brakleen" (Chlorinated solvent) and clean the points and wells completely.