On the Subject of Double Arrows

It's enough to get you to the boiling point.
Garbage. This was clearly wired up by imbeciles. ★☆☆☆☆

On the module are eight directional buttons pointing in four directions, a black reset button, and a display screen in the center.

Initially on this display is a two digit number; this is the starting position in the grid below.

Each of the eight buttons will move your position in the grid in one of the four cardinal directions, these directions may not necessarily be the directions the buttons themselves are pointing.

    However:
  • Inner buttons will always move 1 space.
  • Outer buttons will always move 2 spaces.

The eight buttons can pressed once each to change the displayed number.
Due to a fault, once a button has been pressed, the display will only show the digital root of the new position.

Once all eight of the buttons have been pressed once, you will have returned to your starting position and the screen will turn off.

    From this point:
  • If there is an even number of batteries on the bomb, move to the position that is one higher than your current position, unless you are at position 81, in which case move to position 01.
  • Otherwise, move to the position that is one lower than your current position, unless you are at position 01, in which case move to position 81.

The module is solved when the tenth valid move is made.

Your position will not change if an invalid move is made.

518060796109084950
527753783435474846
217518743736383945
207619733372304243
222317163215314044
252465667071294128
035764566314121302
265859676968070627
048154556210110501

Note: This grid is a flat torus; the parallel sides of the grid are connected.