A Magic Two-Giraffe Tour!

I've returned to doing some work on tours and other mathematical recreations after a break of a few months. I revisited the proofs I published in 1976 beginning in the second issue of Chessics that closed and open Giraffe tours on the 8x8 board are impossible. This led me to find two 16-move closed tours of the A1-B1 cells and two 16-move closed tours of the A2-B2 cells. In each case one tour is symmetric and the other asymmetric. There are also 16-cell open tours possible of course. Two such tours can be joined to form a 32-cell open tour. I have combined two copies of such a tour to form a Magic Two-Giraffe Tour, where the link 32-33 is a rook move:

15 46 11 42 23 54 19 50
24 53 20 49 16 45 12 41
01 36 05 40 25 60 29 64
26 59 30 63 02 36 06 39
47 14 43 10 55 22 51 18
56 21 52 17 48 13 44 09
33 04 37 08 57 28 61 32
58 27 62 31 34 03 38 07

I composed this tour just this morning (Wednesday 9 October), using the two symmetric quarter tours. Must now check whether any others are possible.