Yup, you're right! The algorithm works like this: (each "move" is an implicit "continue" in the pseudocode)

    while no checkmate:
        If your rook is about to be taken, move it to the other end of the current rank.
        If the enemy king is on rank n and your rook is anywhere but rank n-1, move your rook to rank n-1 (unless it can then be taken, in which case move it to the end of its current rank.)
        If your king is anywhere but rank n-2, move towards there.
        If your kings are on the same file, advance the rook to rank n (unless it can be taken...)
        If |file of your king - file of opponents king| is odd, make a wasted move with the rook (keeping it on the same rank).
        If you've gotten this far, move your king towards the opponent's king (staying on the same rank n-2).