Mark: don't teach Timmy that he has to bite harder to get what he wants.
(you to stop)
It's the natural thing to do: first give a small warning, then a larger, then an even larger one etc.etc. till (painfull bite) you get one you can not ignore.
Once they find they have to go all the way to get the desired reaction from you they will start to skip the first fases completely (because they are not working anyway) and you get "a bitey parrot, who wil lash out out of the blue".
(that happens a lot! Reason number one for rehoming- next to screaming of course )
Have you read the 'bitepresure' tread?
http://www.parrotforums.com/training/63988-bite-pressure-training.html
(just had it open myself)
Birds communicate bij movement first and using their beaks second.
Really look for it an you'll see before Timmy grabs your finger there wil be a few (very short) moments of extra stillness (like him holding his breath).
It is annoyingly subtle, but it is there (I miss it a LOT) - that is the first warning, saying "Ehm...I've had enough, thank you, now plze stop doing that" (at least on that particulair spot).
It is okay to miss that- we give scritches a lot and are not always 100% focussed on them- (I read the screen while cuddling parrots or watch tv) so this is where the "gently"-reminder comes in.
I find it okay to have them use their beak to move the hand/ finger away, but not in a bitey way!
So instead of encouraging harder bites (and they *will* reinforce the message if you do not respond to their polite request to let go/ stop --it's a DNA-thing) let them know: "Hey- I heard you, but TONE IT DOWN!"
So usually I will tell them "gently", offer my finger again so we can figure out how much pressure is acceptable.
Nowadays the macaw is being very random about it (only been here about 5 months and she has other issues), but the greys will just touch, sometimes hold and push of... if they *really* are in no mood to (example) step up they give my hand a very dirty look first and then (Appie esp.) use just a little too much force just to show me she is NOT enjoying this but not really biting, she just grabs hold and gives me a clothespin-pressure-like pinch for a few seconds.
(And that is the max of her acting out her displeasure. She made her point, I got it - everybody is happy.)
Learn his bodylanguage (he probably already mastered yours) and work on "gently".
You are going to do great together.