XT660Z
2011
~40 000km. Only owned the bike since 20K, so do not know if valves have been checked before.

I opened the tappets and tried to test the state of the valves. I find that the intake valves have their clearances quite OK. On the exhaust side, the top part (the Y-fork bit [edit: I understand from internet search it is called 'rocker arm']) is quite loose, and appears to be moving up and down as if it is loose at a hidden hinge (and moves up and down about 3 mm or so from my estimate [edit: Please see below, it was roughly 0.7mm]). To my inexperienced eyes, this does not seem right.

Has this been experienced by other people in the forum? What is the fix? Or it this what people mean when they say the valve clearance is really out?