This is your gauge and your choice of how to service it.
Personally... I would not spray any oil inside a mechanical speedo or tach. The spindle that supports the pointer is supported on the inboard end by a needle bearing. That bearing is supposed to be clean and operate dry. Any lube, even WD-40, will increase the drag on the spindle coupling it "more" to the magnet assembly. This means initially the gauge will read high. As the oil collects dirt and thickens with age you may find that one day the pointer goes all the way around the gauge face and an autopsy will reveal the return hairspring has been twisted into a knot.
You can Google for the 27 page PDF by Anthony Rhodes that discusses cleaning and calibrating Jaeger and Smiths speedometers. The mechanical tachs are the same as speedometers except for their lack of odometer components. The PDF will walk you through how to clean and recondition your gauge.
I won't argue on LBC units. But, on old, old US marques, a drop of machine oil (NOT 3-in-one) on the spindle in the spinning magnet makes a speedo last, oh, 50 or more years between rebuilds.
Depending on how much you drive, no oil, as little as 10 years and it's "kicking", with spindle out of line and magnet catching bowl.
All of mine are oiled, the Jag is when I took the speedo apart anyway.