I'm not sure, after carefully reading the Illinois law, that residents of Indiana will even be allowed to apply for a non-residence license to carry in Illinois.
Non-Resident Permit
Non-Resident License Applications.(a) For the purposes of this Section, "non-resident" means a person who has not resided within this State for
more than 30 days and resides in another state or territory.
(b) The Department shall by rule allow for non-resident license applications from any state or territory of the United States with laws related to firearm ownership, possession, and carrying, that are substantially similar to the requirements to obtain a license under this Act.
(c) A resident of a state or territory approved by the Department under subsection (b) of this Section may apply for a non-resident license. The applicant shall apply to the Department and must meet all of the qualifications established in Section 25 of this Act, except for the Illinois residency requirement in item (xiv) of paragraph (2) of subsection (a) of Section 4 of the Firearm Owners Identification Card Act. The applicant shall submit: . . .