I assume the longer the V part of the Y, the more the tail will be able to transfer corrective effect to the kite?
Interesting question. My first thought is no... in fact probably the opposite. Although it might have that effect if the Y-line were actually a tail rather than a line.
The reason the Y-line is so effective is that it acts from a point central to the trailing edge and not very far from the trailing edge. So a pull on one side of the line doesn't just pull that side of the kite rearwards, it pulls it around towards the centre. The kite rotates around a point close to the centre of the trailing edge.
If each side of the V were long, the rotation point would be quite some distance behind the kite. Instead of the kite being quickly rotated back towards the centre, it would more likely be dragged sideways with a much smaller amount of rotation. This would lead to a kite which doesn't rotate so much from straight into the wind, but sweeps in a wider arc slowly back and forth across the sky
While I'm at it, your thoughts on U tails?
U tails have a very similar effect to single tails on a Y-line. As a kite rotates away from straight into the wind, the side of the tail which has been pulled forward becomes longer than the side that has fallen backwards. Because it is longer, it creates more drag than the section of tail attached the other side of the kite. This drag pulls that side of the kite backwards until the kite points straight into the wind and the two sides of the tail are equal in length again.
Talking about U tails, this got me thinking about the arrangement where you have a U tail with a single additional piece coming off the middle - effectively creating a Y tail, but with the whole Y adding drag instead of just the central leg. How do you think that would compare to the Y arrangement where just the middle leg is adding drag?
I've seen this used very effectively on some German rectangular soft kites that have no keels. For want of a better description, the kites are effectively inflatable Della Portas. DPs traditionally have (and need!) a loop or U tail
Will any of this logic change if you go from a flowform, pilot, etc to a delta, rokkaku, conynne, etc?
No, the logic doesn't change. But it gets affected by how far apart the mounting points are for the tail/loop, and whether the kite can have the mounting points at the very rear of the kite. So, not particularly useful on a diamond