Removal. All signs shall be removed by the owner or lessee of the premises upon which the sign is located when a business which it advertises has not been conducted for a period of six months or when, in the judgment of the Village Board, such sign is so old, dilapidated or has become so out of repair as to be dangerous or unsafe, whichever occurs first. If the owner or lessee fails to remove it, the Village Board may remove the sign at cost of the owner, following adequate written notice. The owner may appeal the Village Board's decision to the Zoning Board of Appeals.