I wish I had an answer for you. I do think tmad had a useful insight. My son was prone for quite a while to go with what we had taken to calling auto-wipe, ie what happens when you don't wipe and let your undies do it for you. GROSS. I guess we nagged enough, and forced him back in the bathroom enough after seeing poop without paper in the potty (he doesn't flush, either) that he finally decided to solve for himself whatever issue he had with wiping. Oh, and he didn't like the itchy rashes he was getting. THAT was probably the biggest incentive to fix the situation, lol. Mother nature. Learning first hand that the stories mom and dad tell are true.
Flushing is another story. I think flushing freaks him out a bit. I can only HOPE he understands our messages about why it is ESSENTIAL to flush when at school or out in public. I THINK he does. He SAYS he does ... but ...
If my son doesn't wash his hands, I send him back. I've explained it a million times, I charged fines for not doing it, and I've finally decided I simply have to enforce it. Listen to see if he washes, check his hands, and send him back if he doesn't wash. I've explained the reasoning, I've asked him to explain what his issues are with it, but we seem to simply be locked in a battle of wills on that one.
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Mom to an amazing young adult AS son, plus an also amazing non-AS daughter. Most likely part of the "Broader Autism Phenotype" (some traits).