Cursor movement in vertical text

[r12a]

In what direction should the cursor move when clicking on the LEFT, RIGHT, UP, and DOWN arrow keys?

Should the UP and DOWN arrow keys move the cursor up and down the line, respectively?

Should the LEFT and RIGHT arrow keys move the cursor left and right, respectively, or should they follow the logical direction of the lines — ie. LEFT moves right, and vice versa? (It seems that some non-Web apps may do this. It may, however, lead to complications in pages that include both Chinese and Mongolian.)

There's a test page that can be played with, courtesy of @aronsoyol, at https://aronsoyol.github.io/caret_test/

Currently, Gecko and Blink browsers move the cursor in the same direction as the arrow on the arrow key, but WebKit is rather odd. It moves up and down the line when pressing the LEFT and RIGHT arrow keys, but appears to get stuck at times. The UP and DOWN arrow keys move the cursor left and right, respectively, regardless of the direction in which lines are stacked.