I believe this is a more complicated question than first meets the eye.
Bespoke hydraulic oils are a relatively recent thing - fifty years ago industrial machinery lubrication products were still a bit basic and the designers began to take advantage of the improvements being made to engine oils (anti-wear additives, oxidation inhibitors, corrosion inhibitors, detergent properties, anti-foaming additives, multi-grade performances etc.). So it comes as no surprise that an old machine is asking for a crankcase type oil.
This is quite a thin oil (in hydraulic terms) but it does have some special characteristics that make it suitable for use in metal-metal type variators (a form of mechanical "continuously variable transmission" gearbox). It is also the case that the low viscosity might have been selected because the fluid is also used for the lubrication of close tolerance high speed bearings - just the sort of thing you would expect to see in a grinder. Is it the case that the fluid is also providing lubrication for the high speed shafts?
I would guess that if all you needed was a thinnish "hydraulic fluid" (do check all around that there isn't a variator in the system) then you should go for something like an ISO VG10 (fluid viscosity = 10 cSt at 40 degrees C/100 deg F).
If you do need the special characteristics for use in a variator then it looks like a suitable alternative would be "Shell Morlina S2 BL 10". Various variator gearbox manufacturers suggest this but warn that no suitable alternative exists: it's Morlina S2 BL 10 or nothing else.
It's difficult to make a comparison between SAE weightings for oil viscosities and the ISO VG numbers (“VG” just means viscosity grade). This difficulty arises because the two standards specify different temperatures at which the viscosity measurements are made (40 deg C for the ISO fluids and at a "low temperature" for the SAE winter grades - the actual temperature being different for each grade). To further complicate the issue, the ISO grades are based on "kinematic viscosity" and the SAE specifications are based on "dynamic viscosity". The conversion between the two requires the division by the fluid density - which varies with temperature. Different oils have different responses to changing temperatures: some thin out quite a lot for just small temperature changes (these are oils with a low "viscosity index") and others don't change their viscosity as much (these are oils with a high "viscosity index" - oils known in automotive circles as "multi-grade" because they replaced the function of several single grade oils, i.e. one for winter and one for summer). So a comparison of one SAE grade oil with one ISO VG oil needs a knowledge of both viscosity AND viscosity index.
Anyway, I came across one chart for engine oils which seems to lump Mobilfluid 62 into the same category as other SAE10W engine oils. But these are straight oils, i.e. single grade oils. If you use a modern multi-grade oil (such as SAE 10W40) then this will contain an additive (the "viscosity index improver") the job of which is to ensure there is a higher viscosity at higher temperatures than would otherwise be the case. Your machine probably wouldn't have been designed with the multi-grade performance in mind so you will find that the oil will be too thick at your working temperature - it's only really a problem if it is being used for spindle bearing lubrication. The result will be that the higher level of friction causes more heating and the extra heating will continue until the oil viscosity reduces enough to balance out the heat-input effect. The oil life will be shortened if it runs too hot, but you might also find that the shaft bearings become too tight because of the thermal expansion.
Sorry - all in all my answer hasn't been much help. You could try the tribology forum but that place doesn’t seem very busy – maybe they’ve all slipped off somewhere.