(a) If prior to the one year immediately preceding the date of the next general election, a vacancy occurs in the office of a member of the Legislature, the Governor shall call a special election in said district, or at large, as the case may be, within thirty (30) days following the day on which the vacancy occurs. Said special election shall be held no later than sixty (60) days after the call, and the person elected shall hold office for the remainder of the unexpired term of his predecessor.
(b) When the vacancy occurs within one year prior to the general election, the President of the Legislature, upon the written recommendation of the territorial committee of the political party of which the previous office holder was a candidate, shall appoint the person so recommended; Provided, however, That if the previous office holder was not a candidate of a political party as defined by law, the Legislature by a two-thirds majority of its members shall elect a person from said district, or at large, as the case may be, to fill the vacancy.