I don't know whom you may be able to get to help, but I would bet that the government doesn't actually have great data on custom wait time- I've never seen them track someone from entry to pass-through. I strongly doubt they have that.
Rather, I think you may have come upon a really cool opportunity- find a way to track it! You'll have data no one else on the planet has. It's like when Uber starts in a new city- the error on their time estimate starts high and decreases over time. If enough people use it, you'll get really got at predicting the wait time based on the factors you mentioned.
Idea: let the traveler download a free companion to the app. Then the user links to the traveler. Once the traveler lands, they can turn on their phone and let you see location.
The user gets an alert "Bob has landed!" and actually see where the traveler is. Over time, you'll get really great at refining the wait time prediction algorithm. You can ask nationality, etc.
Potential problems: No phone, international traveler can't use phone in destination due to roaming charges, can't have phone on in certain custom areas.