[header] How to suppress the gag reflex [title] Numb your soft palate. [step] When an object touches the soft palate, it can trigger the gag reflex. Use an over-the-counter (otc) throat-numbing spray like chloraseptic to desensitize your soft palate. 
Alternatively, you could gently apply a topical otc analgesic with benzocaine using a cotton swab. The effects should last for about an hour, and your palate will be less reactive.