I thought of behavioral indicators such as number of cancelled appointments, times late, the length of the assessment process, number of clinicians (second opinion). I would greatly appreciate ideas or research experience.
I think asking them directly would be a valuable way of finding out what impacts on ability to take part in the diagnostic process. Cancelled appointments and being late might not reflect compliance as there may be a number of factors impacting on capacity to make appointments - change of address so didn't get schedule, work commitments, stress, child care, language barrier, etc. Relevant questions might be - who initiated the process - parents or outside agency / professionals? Was there a clear pathway to diagnostic referral? Did parents get information? Does the child have a prior diagnosis? Does a sibling have a diagnosis? Do the parents think the child has ASD? What do parents think can be gained from getting a diagnosis for their child?
A qualitative measure like interviewing them could be used. You can then analyze the data through coding, and if you use a Likert scale, you could apply a statistical analysis. I think the behavior indicators you mentioned are good, but you could turn them into statements in a Likert scale and then have the parents rate the questions.