From the Jacksonville Ordinance Code, Ethics sections
Section 602.408 Prohibits APPOINTED City officials (including Boards, Commissions, and Authorities) who were required to file "Form 1 Financial Disclosures" from lobbying the City (etc.) for a period of 2 years. So this doesn't seem to apply to the elected Mayor or Council.
Section 602.411 seems like it might apply here.
602.411 Disqualification of former officers and employees in matters connected with former duties or official responsibilities; disqualification of partners.
(a) It shall be a violation of this Chapter for any person, who was an officer or employee of the City or an independent agency, after his or her employment has ceased, knowingly to act as agent or attorney for anyone other than the City or an independent agency in connection with any administrative or other proceeding, application, request for a ruling or other determination, contract, claim, controversy, charge, accusation, arrest or other particular matter involving a specific party or parties in which the City or an independent agency is a party or has a direct and substantial interest and in which he or she participated personally and substantially as an officer or employee, through decision, approval, disapproval, recommendation, the rendering of advice, investigation or otherwise while employed by the City or an independent agency.
(b) It shall be a violation of this Chapter for any person, who was an officer or employee of the City or an independent agency, after his or her employment has ceased, to appear personally before any unit of government as agent or attorney for anyone other than the City or an independent agency in connection with any proceeding, application, request for a ruling or other determination, contract, claim, controversy, charge, accusation, arrest or other particular matter involving a specific party or parties in which the City or an independent agency is a party or has a direct and substantial interest and which was under his or her official responsibility as an officer or employee of the City or an independent agency at any time within a period of one year prior to the termination of his or her responsibility.
Subsection (c) provides a mechanism for the "head of the unit of government" to grant an exception if the former city employee is a subject-matter expert in the matter before the city or agency.
However, this section appears to be most on point, but it has lots of conditional language that might provide loopholes.
Sec. 602.412. - Prohibited future employment.
It shall be a violation of this Chapter for any person, who was an officer or employee of the City or an independent agency, after his or her employment has ceased, to be employed by or enter into any contract for personal services, with a person or company who contracted with, or had a contractual relationship with the City or the independent agency, while the contract is active or being completed, or within two years of the cessation, completion, or termination of the person's or company's contractual relationship with the City or the independent agency, where (1) the contract with the City or the independent agency had a value that exceeded $250,000, and (2) the officer or employee had a substantial and decision-making role in securing or negotiating the contract or contractual relationship, or in the approval of financial submissions or draws in accordance with the terms of the contract; except that this prohibition shall not apply to an employee whose role is merely as a review signatory, or to contracts entered into prior to January 1, 2008, or to contracts that have been competitively procured. With respect to this subsection a contract is competitively procured if it has been obtained through a sealed low bid award. A "substantial and decision-making role" shall include duties and/or responsibilities that are collectively associated with: (i) approving solicitation or payment documents; (ii) evaluating formal bids and proposals; and (iii) approving and/or issuing award recommendations for final mayoral, City Council, or independent agency approval. The contract of any person or business entity who hires or contracts for services with any officer or employee prohibited from entering into said relationship shall be voidable at the pleasure of the City or independent agency. This prohibition shall not apply to any former officer or employee after two years from cessation from City or independent agency employment. An officer or employee subject to the prohibition of this Section who believes his or her role in the applicable contract does not create an ethical dilemma, may appeal to a committee of the City Council Rules Chair, the Chairperson of the Ethics Commission, and the Chief of Procurement for relief from this Section. Said appeal shall be considered and ruled upon within ten business days of a written request.
The Ethics Code:
https://library.municode.com/fl/jacksonville/codes/code_of_ordinances?nodeId=TITXVIJUCO_CH602JAETCO