Autism and gender id:
The "triad of impairments" is at the heart of autism.
Repetitious behaviour/ special interest/fixation on the same thought patterns.
Impaired social communication.
Impaired social imagination.
With gender identity, an autistic person can get fixated on the concept of trans, and it can become one of their special interests.
Impaired social communication leads to autistic people understanding words like "boy", "girl", "kind", "sex", "gender" in a narrow, rigid, way. Without understanding the social context, the autistic person finds it difficult to notice when people are saying something they don't believe, or using words with a subtly different meaning, or mixing up "sex" with "gender".
Impaired social imagination leads to autistic people acting without accurately envisaging the social consequences. Neurotypical people seem to have a magic ability to quickly predict how other people will interpret behaviour, actions, and words.
Thus an autistic child may become fixated on changing to the opposite sex or gender and spend all their time thinking about it, from the moment they wake until they fall asleep. Or they may merely hold very firmly to the idea.
When adults "be kind", and call the child "brave", the autistic child doesn't notice the pity implicit in those words, nor the warning.
Most children can't imagine the consequences of medical treatment, but neurotypical kids are better able to predict the many social consequences of each aspect of transition, or of transition as a whole.
I am certain there are other reasons a child may say they are trans, but I think this is why autistic children are overrepresented. Since autism in girls is often overlooked until puberty (or adulthood) and the waiting list for autism assessment is years, it may well be that more gender dysphoric girls are autistic than the official figures suggest.
Idk if anyone has written anything more scholarly along these lines.