I see. I thought that the sequences of numbers are read off as the sequence of different squares that the fish is in (i.e. the instance the fish goes to another square, the square's letter is added to the sequence). This 'moment' thing is going to make things messy.
My impression is that
1) The bottom of the pool is divided into two rows of squares. The squares are touching one another at the sides or the verteces. So at any momment, the fish HAS to be in one of the squares.
2) The fish is swimming aimlessly along the pool. Suppose that we define the current position of the fish by vertically projecting the fish's center of mass down to the bottom of the pool.
3) If we imagine the track that the fish's center of mass makes as a line making a random walk, the probability that the line crosses the square's vertex over to a diagonal square as opposed to crossing a side is 0.
Please correct any of these assumptions if they are not in accordance to the OP.
Some clarification. Do we assume that the goldfish has zero size? Suppose the fish is in the top row in Square B, like this illustration
A B C ...
N O P ...
He can cross over to A, go over to C, or down to O. However, if the goldfish has zero size, he possibly can cross over the diagonal and go to N or P. Although the chance of that is also effectively zero, even assuming that the fish has zero size. So, essentially, the question is "can the fish cross over to diagonally connected squares?"