For this trip, you should make sure you pack a few essentials.
1- Make sure you bring the clothes I mentioned earlier. You don't want to stick out in the past!
2- For when you're not in public, you might want to make sure that you bring good summer clothes. It's very HOT in El Paso so it's best if you are ready.
3- Of course, bring sunscreen. You don't want to go back to your family red as a tomato!
4- Bring nice clothes in case you go out.
5- Bring running or walking shoes since you might end up walking a lot. Transportation wasn't the same in the 1920's so be ready to walk a lot!
6-I recommend you to bring a bathing suit. Swimming is a very good way to cool down in the intense El Paso heat.
These are simple things that I personally, as a hint to the reader, recommend. El Paso heat can be extremely hot. They're not eighty degree summers. Not ninety. They can reach up to ONE HUNDRED DEGREES! That's why I personally (STRONGLY) recommend that you bring these things.