Just for background. Headspace checks are required on new rifles because of the wide tolerance spread on ammunition, especially military ammunition in wartime. A GO gauge ensures that the rifle will accept a cartridge on the outer (longest) end of the tolerance. A NO-GO gauge ensures that ammunition on the inner (shortest) end of the tolerance will not be allowed to stretch far enough for the case to separate. The FIELD gauge ensures that wear and tear on a used rifle has not progressed to the point that case separation of short cartridges is not only possible but likely.
In truth, even case separation is not a very serious problem in the civilian world. Rarely is there any serious gas escape, and the worst result is usually a trip to the gunsmith to have the forward part of the case removed. But in combat, a separated case would mean a disabled rifle and possibly a dead soldier, which is why the military takes rifle headspace concerns very seriously. But separated cases with machineguns (especially the Brownings) was so common that headless shell extractors were common issue to machinegun crews in the U.S. service.
So, how and why does headspace become a problem? When a rifle like the Mauser leaves the factory, the headspace will be correct. As a rule, the barrel is made with a short chamber; after it is installed, the chamber is reamed until the headspace is correct. Exactly how that is done varies with the factory and the rifle. But as the rifle is fired, the bolt lugs and the lug seats in the receiver become battered, and operating the bolt induces wear, especially in dusty or sandy areas.
So, is it necessary to check headspace on your milsurp Mauser? Probably not; "first world" armies kept their equipment well maintained, and few "lesser world" countries fired their rifles enough to create excess headspace. If you want to check, do you need all three gauges? No, you need only the FIELD gauge. The GO and NO-GO gauges will be needed only if you plan to rebarrel a rifle, using a new barrel.
What if you want to use a "take off" barrel as a replacement? If the headspace is too tight, using a reamer to set it is easy. If the headspace is excessive, then you have a problem. Most folks will say that "all you have to do" is to set the barrel back a turn and rechamber. But on a rifle like the Mauser, that will mean you have to adjust the stock so the bayonet will fit, and adjust the front band and spring, plus the stock cuts for the rear sight and barrel steps won't line up. On a rifle like the M1 (Garand) setting the barrel back will throw off the gas cylinder and operating rod, as well as the upper handguard and the band. That means major work, plus you end up with an odd-looking rifle.
Jim