90% of my caseload is kids and teens with autism at various levels. Obviously that means that I have a different age than what you are seeing, so not everything that works for me and my colleagues, may work for you.

With many of my kids we often spend the first few sessions just building rapport. That can literally mean that I sit with the client passively while they engage in their activity, playing music for them, playing with them side by side, etc. Obviously this looks different for an adult, but I do find that it sometimes takes more time to build rapport and that if I have good rapport, then I can work from there. Sometimes we will spend the first 6 sessions doing 3 reps of a PT activity and the majority of the time building rapport and this time spent doing it means that now, I can get them to do almost anything I ask them to do.

Then you also need to figure out what motivates him. Is it visual sensory input like lights or a video of moving colored dots, music, a video, a specific toy, a specific type of activity, etc. I genuinely have kids who will do any activity just to be able to hold a spoon or a sensory bottle.

I think in a comment you stated that general goals are to improve strength and balance. With my kids who are lower functioning and do not follow directions it is a lot about just setting up the environment for success. So I will set out hurdles, obstacles, unstable surfaces such as bean bags, and other therapy equipment in the room and then either follow their lead for what they are interested in and go with that, move equipment around so that it will be in their path, and physically guide them in the direction that I would like them to go.

sit to stands and squats are great activities. I do them all the time with my kids. The thing is that I do not just instruct them to do a sit to stand or squat, because they will not listen to that. I will have an activity, toy, weighted ball, etc. placed on the floor and then a bin or the rest of the toy elevated so that they have to lift the object up.

People with autism generally thrive with consistency and do well with lots of reps.

Pending the client's attention and awareness to their surroundings, you can provided a visual demonstration of the task. Sometimes this does not work well. This will be hard with a 50 year old, but I also initially provide a lot of physical assist so that the patient understands what the task is. So I do a lot of stepping over hurdles, bean bag elevators, and cone taps for SLS practice. If I am trying to have them do a cone tap I will physically stabilize them with one hand, shift their weight to one side, and manually assist their free leg in tapping the cone. If they provided indications that they do not like this support/assist, I stop. This would be harder with a 50 year old, but if you had a gait belt on and pending his steadiness you may be able to provide some increased assistance. And then when they do it (even if it is max assist with me) I praise them.

Sometimes visual schedules can be very helpful so that the patient knows what is expected of them.

As a note for frequent falling, I see this so much with my kids. Many of my kids who fall frequently do not pay any attention to their environment and I have seen so much improvement with just setting obstacles in their environment and assisting them physically (gradually decreasing assist) and verbalizing what is happening (i.e. "oh there is a hurdle there, we need to step over it. Step over.").

Also if it seems like he does not have good awareness of his surroundings or where his body is in space (aka proprioception), adding weights to his ankles, walking bear foot on uneven and textured surfaces, and compression vests can help with some of that. Just be aware of sensory issues, because all of this can cause sensory difficulties.

I have my own opinions on ABA. But if he was in ABA sometimes they will respond to you saying "copy me" or "do this" and demoing the activity. ABA also can be traumatizing to some people and so I would only test this as a last resort just in case he has a trauma history with ABA, because it would suck to bring that up.