Your result
Likely
On what you have said, you are a Thai citizen already, and have been since the day you were born.
Thai nationality passes from parent to child under section 7(1) of the Nationality Act. Where both parents were Thai when you were born, none of the awkward questions arise: it does not matter where you were born, whether your parents were married, or what year it was.
This is worth being precise about, because it changes what you are asking for. You are not applying to become Thai. You are asking Thailand to record a nationality you already hold. There is no deadline and no age limit on doing that - people register for the first time in their forties and fifties.
What happens next: the document that unlocks everything else is a Thai birth certificate. If you were born outside Thailand and your birth was never registered with a Thai embassy or consulate, that is the first step, and the embassy for the country you were born in is where it starts. With the birth certificate you can be added to a house registration, the tabien baan, and from there apply for a Thai ID card and a Thai passport. Expect to produce your parents' Thai documents; if they are no longer living, or their papers are lost, the district office will look for other proof of their nationality, and DNA evidence is accepted in Thailand to establish a parental link.
Two things people usually want to know. Thailand does not require you to give up your other nationality: a person Thai from birth keeps both, and the provision about declaring at twenty carries no penalty and is not enforced. And if you are male, Thai nationality carries a military service obligation - registration at 18 and a conscription lottery at 21 - which applies to dual nationals as well, and which someone acquiring Thai nationality after the age of 46 is exempt from.