The inheritable signature consists of the seven IV bits that, in GSC, are always faithfully passed down from one parent or the other. All seven of those bits are included among the 13 bits that the game checks to have specific values for the shiny mask, so if the egg inherits anything other than an exact 7-out-of-7 match with that mask, there are no values that the remaining 6 bits could possibly have to make up for it.
GSC, unlike any future games, included an attempt at an "anti-incest clause" in breeding, which it can at least attempt to track by the nature of this inheritance system. If both prospective parents have the same value in all 7 of those bits, it will say the Pokemon are "brimming with energy," and refuse to allow any eggs to be created.