Let's define 2 different sharpening conditions: one where you're operating within 95% of the keenness your hone can provide, and one where you operate near the limits of what the hone can do.
In the first situation on a Coticule, it doesn't matter what you do, as long as the blade remains in proper contact with the surface of the hone. Circles, figures of 8, halfstrokes, it's all good. Some are of course easier to hone the blade evenly along its length, but as far as steel removal is concerned, It doesn't matter.
In the second situation, we're trying to squeeze the last bit of keenness out of the Coticule, and during this stage we are shaping the last bit of the very edge, the part that will eventually define the quality of our shave.
Because you're aiming for the maximum of what the Coticule can provide for keenness, you can't afford anything that would hold it back.
This calls for:
- low and consistent pressure (that "consistent" is often overlooked)
- strokes that intermittently work both sides of the edge, to minimize any bur formation
- no use of slurry
- the avoidance of edge trailing strokes
This last statement perhaps demands further explanation. Bur formation is a process that depends on the displacement of steel, caused by deposits of steel debris and by a plastic deformation at the surface level of the steel. Note that at the thinnest part of the very edge, the steel is not much more than "surface", hence this plastic behavior becomes rather important. This bur displacement takes place in the trailing direction. That's why it's better to hone with the edge leading. Otherwise the very tip will exist out of bur-like steel, with excellent keenness but poor durability. This explains why pasted stropping induced keenness reverts back so easily to its previous state.