It is more accurate to time a fixed number of swings than it is to count the number of swings in a fixed time. If you count the number of swings in 30 seconds, for example, it is unlikely that there will be an exact number of swings. How do you work out accurately the last incomplete swing? Was it exactly one quarter of a swing, or a little bit more? You do not have this problem if you time complete swings only.
Using the centre rather than the top of the swing for timing is also more accurate. At the top of the swing the pendulum is moving slowly and changing direction. This makes it difficult to judge exactly when the bob has reached the top of the swing. When the bob moves through the centre it is moving quickly and in a single direction. This provides a more reliable visual reference point.
An alternative method to use is to set up the pendulum such that it dangles over the edge of the bench. A reference mark is placed on the edge of the bench at the centre of the swing. When the pendulum passes this reference mark the timer is started/stopped.