Fencer: The point of counting is to obtain a draw. Counting is voluntary. Stopping to count is voluntary too (in case you change your mind and don't want a draw anymore). This much seems to be clear.

Couldn't you simply interpret the rules like this: Whoever starts counting, thinks he's at a disadvantage. That means that theoretically, both players could count if they wanted to - but they would probably both be happy with a draw in this case!