Guenter Stertenbrink reports that after a computer search
there are no symmetric magic knight tours on the 8x10 rectangle.
8x10 magic knight tours - ChessProblem.net
He provides this example of a rotationally symmetric magic tour 8x12.
First half numbered 1 to 48 (instead of 0 to 47).
Rank sum 582 (6x97). File sum 388 (4x97).