Originally Posted By: Crazyville
It seems everything I ask, he either declines outright or neglects until I deal with it myself.


This likely comes from his expectations. He has confident expectations that what ever he does, will not be good enough. Even if he does it, you will not be happy.

Originally Posted By: Crazyville
He has started filling my gas tank for me. It's not something I can't do myself, or something I can depend upon him to do regularly, but does that count?


Yes, that counts.

If you cannot provide him with tasks which he WILL accept, he may reach out in ways that he feels he CAN contribute.

Look for these things and appreciate them. As you let him know you appreciate them, no matter how small or insignificant you may feel they are, he is likely to step in more. Again, praise the positives. Like a child, the more praise you give him, even for attempts, the more likely he will want to do more. Your praise would suggest to him that you are happy... and he wants you to be happy...

If he takes on a "honeydo" task, do your best to not verbalise any flaws in his workmanship or how he may have failed to complete the task to the extent you had hoped. Thank him for doing it and make a note not to ask him to do a similar task in the future.

What IS your H good at? What are his strengths?