It was so fascinating to see those stress patterns that I just had to play a little more. This time, the goal was to simulate the gap between a cap and a pivot jewel such as found on a balance cock. The top of a pivot jewel is slightly curved and the bottom of a cap is flat. When oiling balance pivots, the goal is to provide sufficient oil to form a ring of oil around the end of the pivot between the jewels.
Another blob of motor oil was placed between the crystals not far from the middle and two clothes pins provided the necessary fringe pattern to simulate the juxtaposition of a flat surface and a curved surface. Sure enough, the blob headed for the thinnest gap - albeit very slowly, The pics below show the position after 6 hours elapsed time (that radial shadow line is a deep scratch outside on one of the crystals):
It appears that there comes a point where the blob stops moving, since it did not go all the way to the center. This point is likely when the molecular attraction force between the oil and the surface of the glass is equal to the motion force that is due to the decreasing gap (or gap force gradient). When the gap decreases the oil spreads out, thereby increasing the attraction force between the oil and the surface. Also when the fringe lines are wider, the gap gradient is smaller.
These experiments have shown quite conclusively that oil tends to move to the narrowest gap and stay there. So fears of random oil migration if a watch is left in drawer are groundless. By the same token, running a watch occasionally to "spread the oil around" is a waste of time IMHO. Also, since the oil moves as a blob, insufficient oiling will leave dry zones - not a good thing.
Sorry about the terminology, I never really studied capillary action or tribology for that matter!