What to visit to experience the real Texas in Houston?

Howdy 🤠 We will be visiting Texas in October flying into IAH. We will be in Houston for 4 nights including a day trip to Galveston and then drive to Austin, where we stay another 4 nights before heading back home to Germany. We’ve been to Hawai‘i, Washington State, Colorado, Utah and SoCal before and now want to experience the rural USA, the Cowboys, the Rednecks, the Trump voters, the NRA supporters and a lot of great BBQ and unlimited refills. All things why America is such a great country. Can you give us recommendations on great authentic American places that we should visit that are not as popular as State Capitol or Space Center? Some texan food spots, maybe events taking place mid October or anything that we can consider visiting? Also some unique shops that you would only find in Texas e.g. western wear outlets etc? I honestly don’t think there’s much sightseeing to do so we’d appreciate any recommendation where you can really feel a strong Texan vibe! 😄 Thanks 🙌🏼