A bit quiet here. Related to cultural events in Thailand two main themes come to mind.Â
One people are already frequently exploring: religion, in the form of temple visits. It's great taking in the sights at main temples, like Wat Pho, Wat Arun, Wat Phra Kaew (the Grand Palace), and the Marble Temple, but visiting quiet local temples is also nice. You can offer monks daily food offerings just by turning up and presenting easily packaged food offerings for alms round between 6 AM and 6:30, at any temple. Or any religious holiday has normal observance ceremonies, which visitors are welcome to join. A main temple like Wat Pho charges a 100 baht entry fee (maybe higher now), but for most you can just walk in.
Other local events are great to visit and experience. An example is the large Red Cross sponsored fair, last year held at the Lumphini Park. There are similar types of smaller events all around, in lots of local neighborhoods. My wife and I attended a street art festival not so long ago in an old neighborhood outside of the main temple area, beside Wat Pho and the Grand Palace. Night markets aren't so different from this kind of theme, but they're not the same thing. Those are just for vending, and fairs or festivals typically also include unique decoration themes and music, or dancing shows, and so on. Something along the same line is commonly associated with Thai holidays, like Loy Krathong. We've visited Light and Sound festivals held at Sukhothai and at the Thai replica park area outside of Bangkok.
It would be hard for visitors to learn of such events, even if they were happening quite close to where they stay. Joining the right Thai online groups, or following the right information pages could help, but in general Thai tourism groups wouldn't mention these kinds of things. It would take a lot of Google search to turn them up, or insider references.
Something like attending a muay Thai kickboxing event would be different from these main cultural events. It wouldn't be for everyone, but those would be easy to identify and reserve, through one of the main boxing event halls, like the Lumphini or Rajadamnern stadiums. In the past these were quite inexpensive even for foreigners, but now they tend to charge more for them. It's nothing like attending a soccer, basketball, or football match, but several times over what locals would pay for admission.