A stone 8 pin is caused by too little deflection.....very similar to a 9. Ball drives the pocket without deflecting and takes the 5 pin straight back (instead of it going and taking out the 8 pin like it is supposed to)
http://www.youtube.com/watch?v=APaxT5KMwhc&feature=youtube_gdata_playerThis video shows the headpin interfering but the end result is still the same. 5 pin straight back instead of going left to collect the 8 pin. Now imagine for a second if that same shot were a touch higher in the pocket. You would see the same extra drive that has the ball taking out the 5-8 and leaving the 9 pin.
Very similar shots overall. Now that said, I won't adjust much on an 8 pin leave as I think it is a true tap and I am in a very good pocket location. But a 9 pin I will move 2-1 left to loosen up the pocket and stay ahead of the transition. (I would rather leave a couple soft 10's than to stay there and see 4-9 or Greek Church)
Here is video of a weak 10 pin. This is caused by the ball being a bit light, but more importantly the ball is still in the hook phase (wide misses that recover) or has rolled out (usually from finding too much friction up front).
http://www.youtube.com/watch?v=nRlEtA2I4VA&feature=youtube_gdata_playerThere are multiple reasons for this weak hit so there are multiple ways of coreecting it. Usually a slight move right is the easiest way. This puts the ball in a higher pocket location and decreases deflection off the head pin. But sometimes a ball change is necessary if the heads are scorched. These examples often lead to "swish" 7 pins for righties too as the half pocket shot and weaker inertia of the ball cause the headpin to hit the 2 pin slightly on the front side instead of at a 45º angle. The lack of inertia from bad ball roll phase also contributes again as less energy is imparted on the head pin which causes reduced pin action.
For me, a very basic and general rule is: a fix for corners is to get the ball rolling better and facing up to the pocket. For 8's and 9's....get the ball to delay a tad and facing the pocket a little less. There are many ways to accomplish these things. Basic lateral moves. Forward and backward on the approach. Hand position adjustments. Less or more hit at the bottom of the ball. Ball change. Or....sometimes on the worst nights....just pack your stuff and go home.....lol.
Hope this was helpful. There are more videos available to see the dynamics of balls going through the pins. It is all I look at when I am bowling as it tells me what I need to know to keep striking.
As an aside, the 6 pin is a very good indicator of how well your ball is going through the rack. When watching most ball videos I concentrate on the action of the 6 pin in judging how well a ball hits.