as for the .308 being shorter that still does not mean that you can not use it
You can use a lot of things if the object is to have something that will
probably fire....
you cannot make an 8mm Mauser case from a .308 Win. You can make something that will probably go bang in the chamber, but its not a proper 8mm Mauser case.
Headspacing an "8mm/08" in an 8mm Mauser chamber will be "iffy". The .308 case shoulder is in the wrong place (too far back). If the case is properly held by the extractor, it will fire, and since the overall length of the round still has the bullet lined up with the barrel, it will work (shoot). But the fired case (.308) will have the shoulder blown forward, and won't have much, if any case neck on it.
AND, odds are high that ammo made from .308 brass will not shoot anywhere near the same point of impact as proper ammo.
Firing a .308 in a .30-06 chamber generally results in approximately a 6 inch lower impact at 100yds, compared to 06 ammo. I expect the same thing using .308 cases fired in an 8mm Mauser chamber.
Also, you would not be able to easily reload the fired (in 8mm chamber) .308 brass again, as there is virtually no case neck. You would have to run it through the .308 sizer again, to create a case neck, then expand that neck to 8mm to load it, which is going to work the brass a LOT.
If you were in a survival situation, desperately needing something that will shoot from your 8mm, and you have all the proper components EXCEPT 8mm brass, but you do have .308 Win brass, you could make something that will go bang in your rifle. Other than that far fetched situation, there's no point to it.
Use the right case (06 length can be formed to the right case length), if you need, or want to form brass. otherwise, get the right caliber brass to start with.
Years ago, I picked up a cigar box full of 8mm Mauser reloads with cast bullets (estate sale) 80 some rounds cases were formed from GI SL 52-53 06 brass. They work fine.