Don't know if you caught this in the DE but it looks as if ex-councilman Lance Jack is trying a workaround to get his seat back:
Lance Jack said all too often it feels like he is the only person really fighting for Carbondale’s future, which is why he has decided to reapply for his council seat.
Mayor Cole has asked for applications for the seat and, as I read the above, Jack plans to apply for the seat that he vacated on Oct. 5. As far as I can tell from a reading of the appropriate statute, there's nothing stopping him from doing so.
As I've noted before, there are two statues that may apply here. The first, #1below, appears to apply to cities that elect aldermen or councilmen from wards, the other, #2, appears to apply to cities that elect their councilpeople at large or from the city population as a whole. The difference between the two is crucial because, under #1, if the council rejects the mayor's first two choices, the mayor then appoints one of the two rejected applicants to the vacant position. Under statute #2, it appears the council continues to vote on applicants until it approves one. It appears the council will go with a combination of #1 and #2, with Mayor Cole collecting letters of application and forwarding them to council, along with his nomination:
#1 Appointment to fill alderman or trustee vacancy. An appointment by the mayor or president or acting mayor or acting president, as the case may be, of a qualified person as described in Section 3.1-10-5 of this Code to fill a vacancy in the office of alderman or trustee must be made within 60 days after the vacancy occurs. Once the appointment of the qualified person has been forwarded to the corporate authorities, the corporate authorities shall act upon the appointment within 30 days. If the appointment fails to receive the advice and consent of the corporate authorities within 30 days, the mayor or president or acting mayor or acting president shall appoint and forward to the corporate authorities a second qualified person as described in Section 3.1-10-5. Once the appointment of the second qualified person has been forwarded to the corporate authorities, the corporate authorities shall act upon the appointment within 30 days. If the appointment of the second qualified person also fails to receive the advice and consent of the corporate authorities, then the mayor or president or acting mayor or acting president, without the advice and consent of the corporate authorities, may make a temporary appointment from those persons who were appointed but whose appointments failed to receive the advice and consent of the corporate authorities. The person receiving the temporary appointment shall serve until an appointment has received the advice and consent and the appointee has qualified or until a person has been elected and has qualified, whichever first occurs.
#2If a vacancy occurs in the office of mayor or councilman, the remaining members of the council, within 60 days after the vacancy occurs, shall fill the vacancy by appointment of some person to the office for the balance of the unexpired term or until the vacancy is filled by interim election under Section 3.1‑10‑50, and until the successor is elected and has qualified.