Idaho follows the federal rules for combat zone pay. Pay excluded from your federal adjusted gross income because you earned it while serving in a combat zone, drawing hostile fire and imminent danger pay, is also excluded from Idaho income tax. Your Idaho filing and payment deadline is pushed back 180 days after your last day of combat zone service.
There is nothing to apply for. Exclude your combat zone pay from the income you report on your Idaho return.
Your orders and Leave and Earnings Statements showing the combat zone service dates and the hostile fire or imminent danger pay.