MT's should be no different than the AT's from BFG in fitment...so with stock rally wheels, the 33x10.5R15's will fit with stock suspension on most '81+ trucks.
There are a lot of variables that can affect fitment, but assuming the backspacing is the same on all stock wheels....stock suspension, stock wheels, the 33x10.5's WILL clear on most trucks. Haven't heard of anyone yet that has clearance issues when stock running the 10.5's on these trucks.
The 12.5's are a bit wider when the tire is turned in the wheelwell than the 10.5's (you are measuring from the outside to inside "length" of the tire when turning) so that may be why some fitment issues exist. But non-stock backspacing and bad suspension can also contribute.
Not really sure if you are dead set on the 12.5's or not, so just throwing the 10.5's out there. Some people think they look too narrow, but are no narrower than the optional 31x10.5's the truck came with, and nothing compared to how narrow new truck tires appear to be.
My dads got tires on his '81 that compute out to 34x12.3 or so and clear fine with the later (IFS) wheels, and I have no idea why they clear on that relatively stock (although sagging in the front from a BBC and PTO winch) truck.