I always do, but now you come to mention it i'm not actually sure if i'm right. Although I have never had a comment about it on my score sheet.
Sorry I'm of absolutely no help at all amI?
I always change as I go over the centre line, just as I change his bend, which gives three changes per serpentine. I haven't be critisised for it but I don't know if it is the right way to do it.
For a three loop serpentine it would help the horse if your diagonal was correct with the bend as this will aid balance and although it may not be commented on per se it may effect the quality of the movement in terms of rhythm and the suppleness.
Your diagonal is never noted in your test! I normally end up riding more on one than the other but as long as the horse stays balanced it doesnt matter
Your diagonal isn't noted but to change it over the centre line would give the best opportunity for balance and consistency in your horses rhythm, therefore lessening the risk of losing marks for the movement. I always change mine over the centre line.