Does the thumb move or stay in the same spot ?
The thuimb is the anchor, it remains in the area behind the second fret of the position you are playing in. If you are playing in first position it would be behind the second fret, or if you are in the third position it would be behind the fourth fret. The reasoning behind this is that the force created by pinching the thumb and middle finger together is greater than that created by pinching the index and thumb together. When playing the scale the second finger(middle finger) would be in the position over the second fret. This doesn't apply to the frets on the sound box, since there is no neck to put your thumb on there. The less the thumb moves about the smoother your playing will be, with a more consistent timing and tone, because your hand will not need to counter balance any involuntary movement.
I tend to move it up or down slightly as I move to another string and even fractionally left or right to reach when I'm working closer to the first fret.
This will be smoother if you think of you hand as already covering all the strings and you're just placing your fingers when needed. This is possible by being aware of the stretch of your hand not just coming from between your index and middle finger, but also from between you middle and ring finger. This is overlooked due to the index finger being too dominant and unbalancing the other fingers.
it seems to want to stay put and I pivot the wrist to get to the right spot
Once again, the less movemnet the smoother the playing. The greater stretch in you hand from between your middle and ring finger will allow for your fingers to reach further needing less movement in the wrist. That type of wrist movement is used in the violin, in the guitar the wrist is kept stationary to allow the fingers to move faster.
On the downward pass, should I be leaving the fingers in place till they're need again or is it ok to lift them once the next note is in place ?
I'm not sure how you would be leaving the fingers in place as you move down the scale, since you would be lifting them up to go down, but in going up it's preferable to keep them down, like stacking. The less movement the better and exaggerated spider hands make uneven playing. In going down it's also best to leave the fingers above the string that is being played, thus leaving them on the previous string would not be advised.
any tips on getting that little finger on the top string clean ?
This is also because of the dominance of the index finger. Once again think about the weight, stretch and leverage coming from between the middle and ring finger.
