Section 65B. A person who has filed an appeal from the refusal of assessors to abate a tax on a parcel of real estate under the provisions of section sixty-five who has paid either a sum not less than one half of the amount of such tax or a sum not less than one half the amount deemed to be such tax under the provisions of section sixty-four without incurring any interest charges on either of such payments pursuant to section fifty-seven of chapter fifty-nine who claims to be unable presently to pay the amount of tax remaining unpaid, may, on or before the last date for payment of said tax without incurring interest, file a motion alleging that the appellant is unable presently to pay such amount of tax and that he has otherwise complied with the provisions of section sixty-four relative to payment of such tax and moving that he be excused from the requirement that the balance of the tax be paid or that the time for payment thereof be extended. If upon the hearing of said motion supported by evidence the board finds the allegations to be true, the board, by order, may grant the motion upon such conditions as may be imposed therein, which may or may not require such petitioner to pay, in whole or by installments, the amount of the tax remaining unpaid, as a prerequisite to any hearing on the merits of the appeal. If the complainant fails to comply with any of the conditions imposed in said order an appeal may, upon motion, be dismissed. If the complainant complies with the conditions imposed in said order, the appeal thereafter shall be heard and determined by said board in the manner provided by chapter fifty-eight A. The board may enter such order as justice may require in the manner provided in section sixty-four with respect to complaints removed from the county commissioners.