Sewing machine oil is a petroleum oil, like the oil you use in your car's engine. Petroleum oils creep; when you apply them to a pivot, say, in a short time they spread down the shaft and over the plate the pivot works in. This means oil spreads to where it is not wanted or needed, and leaves the point needing lubrication dry.
Animal, vegetable, and some synthetic oils have the virtue of "staying put". Animal and vegetable base oils, and blends thereof, were used in watches and clocks for centuries until synthetic oils were developed.
Here's a great source of lubricants for fine mechanisms. http://www.ofrei.com/page246.html I've been using these oils and greases for a couple decades and reccomend them very highly.
I thought sewing machine oil would have the best viscosity, but you obviously know much more about oils than me and I apologise for my crass post.