who is, at the time of the miner’s death, disabled as determined in accordance with section 223(d) of the Social Security Act [
42 U.S.C. 423(d)], during such disability. Any benefit under this paragraph for a month prior to the month in which a claim for such benefit is filed shall be reduced to any extent that may be necessary, so that it will not render erroneous any benefit which, before the filing of such claim, the Secretary has certified for payment for such prior months. As used in this paragraph, “dependent” means that during the one year period prior to and ending with such miner’s death, such parent, brother, or sister was living in the miner’s household, and was, during such period, totally dependent on the miner for support. Proof of such support shall be filed by such claimant within two years after May 1972, or within two years after the miner’s death, whichever is the later. Any such proof which is filed after the expiration of such period shall be deemed to have been filed within such period if it is shown to the satisfaction of the Secretary that there was good cause for failure to file such proof within such period. The determination of what constitutes “living in the miner’s household”, “totally dependent upon the miner for support,” and “good cause,” shall for purposes of this paragraph be made in accordance with regulations of the Secretary. Benefit payments under this paragraph to a parent, brother, or sister, shall be reduced by the amount by which such payments would be reduced on account of excess earnings of such parent, brother, or sister, respectively, under section 203(b)–(
l) of the Social Security Act [
42 U.S.C. 403(b)–(
l)], as if the benefit under this paragraph were a benefit under section 202 of such Act [
42 U.S.C. 402].