For the purpose of registering voters under this Article 5, in addition to the method provided for precinct registration under Sections 5-6 and 5-17 of this Article 5, the office of the county clerk shall be open between 9:00 a. m. and 5:00 p. m. on all days except Saturday, Sunday and holidays, but there shall be no registration at such office during the 35 days immediately preceding any election required to be held under the law but if no precinct registration is being conducted prior to any election then registration may be taken in the office of the county clerk up to and including the 28th day prior to an election. On Saturdays, the hours of registration shall be from 9:00 a. m. to 12:00 p. m. noon. During such 35 or 27 day period, registration of electors of political subdivisions wherein a regular, or special election is required to be held shall cease and shall not be resumed for the registration of electors of such political subdivisions until the second day following the day of such election. In any election called for the submission of the revision or alteration of, or the amendments to the Constitution, submitted by a Constitutional Convention, the final day for registration at the office of the election authority charged with the printing of the ballot of this election shall be the 15th day prior to the date of the election.
     Each county clerk shall appoint one deputy for the purpose of accepting the registration of any voter who files an affidavit that he is physically unable to appear at any appointed place of registration. The county clerk shall designate a deputy to visit each person with a disability and shall accept the registration of each such person as if he had applied for registration at the office of the county clerk.
     The offices of city, village, incorporated town and town clerks shall also be open for the purpose of registering voters residing in the territory in which this Article is in effect, and also, in the case of city, village and incorporated town clerks, for the purpose of registering voters residing in a portion of the city, village or incorporated town not located within the county, on all days on which the office of the county clerk is open for the registration of voters of such cities, villages, incorporated towns and townships.