AA now gives you a little form to collect it online, if you bother to ask.

The tax only applies if you stay in Colombia less than 90 days, so you will need to prove that. After 90 days you're considered a resident for purposes of the tax.

I had an Alaska award flight and the AA refund site wouldn't work so I finally filed with Alaska and it did eventually turn up. I showed my incoming passport stamp as well to show I was there less tan 90 days.

Keep on fighting this BS tax!