My question involves a traffic ticket from the state of: TX

I just moved from a college town, Iowa to Houston, TX, and got a new used car.

Yesterday, I was driving onto a highway from a local road with my friend, it seemed that a noise and strong light shined once onto my car. But both my friend and me did not hear very clearly, and continued driving, but felt a little weird since there was a car following us. It is not like a cop car so we were totally confused because we were not speeding. Then to be safe, we left the highway using the nearest exit and then the car became a cop car with colorful lights on. Just after left the highway, I realized that I did not turn on the headlight.

The police did not accept my explanation and gave me a ticket.

The truth was that I did not turn on the headlight.

The reasons why did I unintentionally drive without headlight are:

1. the college town is way darker than houston area, so both me and my friend thought the light was on. If the light is not on, no way to drive in my original town, but not here.

2. The car I bought about one month ago gets its inside dashboard light on once the engine is on whenever day, night, headlight is on or off. This is different from my last car that I must turn on the headlight to turn on the inside light.
That's why it made me think the light was on yesterday night.

Anyway, I admit that I did not turn on the headlight. The police gave me a ticket without fine, just let me go to the court 2 weeks later directly to admit guilty or not. I was a little confused. Usually I should get a ticket with fine directly? what should I do in the court? What are my options?
I have a clean driving history.