Funny old thing, I was was just thinking about this very subject when I happened upon this thread...
I have observed a large range of behaviour from many people over the years, ranging from only touching the controls if absolutely neccessary to hanging on for grim death at all times!
These days I sit in a large FBW beast with (a) very reliable autopilot(s), so I tend towards the former and let go as soon as the A/P is engaged.
I do profess to a (irrational?) slight degree of annoyance when the PF insists on staying physically connected to the aeroplane even when the electronics have taken over. It makes the PNF's job harder as you often find a marked reluctance from the other side to 'let go' of the comforter and make FMC & MCP changes and the like. It also runs somewhat contrary to our SOP's.
My real fascination is with what these guys think they are achieving with their white knuckles (showing through the gloves). I have seen blokes with their hands on the yoke for half an hour in the cruise in light turbulence.
There are two main states of man and machine:
1) A/P out, pilot flies aeroplane.
2) A/P in, A/P flies aeroplane, pilot tells A/P how to do it.
Granted, in the latter stages of a CATIII approach, it would seem to be wise to 'guard' the relevant controls but at FL370?
My point seems to be shaping up thus: If you are happy with the A/P, leave it alone; if you are unhappy, take it out. There is no 'middle ground'.
You cannot instill a idea into the A/P or A/T by pressing on the controls or hanging on the thrust levers. At best, nothing happens; at worst the A/P goes into some other mode (CWS, V/S or whatever) and you don't notice because it hasn't disconnected...
In short, to get the A/P (or any automated system for that matter) to do what you want, use the INTERFACE PROVIDED BY THE MANUFACTURER and follow the protocol demanded.
As I said earlier, it's more a point of interest and I don't really care what other people do. I'm sure the earlier generations of aircraft had to be watched continually and A/P failures were frequent. After nearly 5000 hours on my present model and no A/P dropouts maybe I'm getting complacent...
Keep pressing the buttons.