Loving, consistant firmness is important at this age. For some children, times out and withholding of privileges (or special toys for little ones) is enough. Be careful with "rewards" for "good" behavior. Good behavior should be the expected norm, not something "special" that requires a bribe.
Exceptional good behavior (like after a long shopping day) can be rewarded with a treat.
I raised a hearing child, not a deaf child, so I didn't have that experience with the extra challenges. I am only stating general parenting principles.
Love
Consistancy
Patience
Firmness (not meanness, not harshness, but firmness--it means, don't let the child control the situation)
At least you know that he understands your signing; otherwise, there would be no point in his eye closing.
It would probably be a good idea to nip that in the bud though. He needs to know that is not acceptable behavior before he tries that trick on his teachers at school.
Maybe when he does that, you can swoop him up in your arms and put him in the "time out" chair. Not harshly, but quickly and firmly. Then, when he opens his eyes, pays attention to your signs, he is allowed to get up again.
I am sure some of the moms and dads with deaf kids here at AD have some more good suggestions.