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.
Lubrication is not a matter of viscosity but of film strength. Viscosity is of importance with oils in certain applications such as damping, where the drag imposed by a very thick (viscous) oil may be valuable - say the focussing helicoid on a lens. In applications such as a shutter or any fine, fast-moving mechanism, high viscosity imposes needless and harmful friction and can render some mechanisms inoperable. In cars, too - the days of using high viscosity oils in engines are long past. Modern low viscosity, multiweight oils with very high film strength give better lubrication, reach vital parts sooner from a cold start, and improve mileage - and modern engines are designed with them in mind. The oils suitable for a shutter have much less viscosity than sewing machine oil, they're almost watery.
I can imagine the reaction of a Rolex service agent when confronted with that. ;<0
Typically, Rolex service centers are confronted with utterly worn-out movements. Joe yuppie buys a watch, all he knows or cares about is that his yuppie pals are impressed. So he wears the watch until it stops or misbehaves, by which time it's been running for years - or decades - without proper lubrication. Last I knew, Rolex was charging around $600 USD flat rate for "servicing" - which included a new mainspring, mainspring barrel, second wheel and bushing, parts for the autowinding mechanism, and other parts which typically suffer when the watch is neglected. Then Joe y. badmouths Rolex watches and service. A simple cleaning could be had for around $200 USD, if the watch was sent in soon enough that that was all it needed, say after a few years of wear. I am not a Rolex repair tech, but I do occasionally do work for one when he gets an older watch for which parts are no longer available so I have an "in".