Why did Zechariah's neighbours make signs to him?
It was an unusual practice at the time to name a son after his father, because a man tended to be identified as, for example, (John) son of (Zechariah), i.e., (John), Bar-(Zechariah); and Zechariah Bar-Zechariah would have been strange.
Matthew Henry claims that Zechariah was both deaf and mute (cf. 1:22, 64), so they appealed to him by means of signs. He responded by means of writing (1:63). These two infirmities are often associated with each other (cf. Mark 7:32, 37; 9:25). But here I find the point strained.
Since the naming of the child typically fell to the father, the "crowd" would naturally be gesturing to Zechariah for his validation of Elizabeth's "announcement." Thus, in Luke 1:63 he asked for a writing tablet, which consisted of a wood tablet (a pinakidion) covered with wax.
To everyone’s amazement he wrote, “His name is John.” So why the amazement? Most likely because “John” was not a name used in their family. The proponents of Zechariah's deafness obviously believe that Zechariah was not able to hear Elizabeth’s choice of this name, but, again, this is strained exegesis. Since Zechariah was mute, he could not “say” anything. His only means of confirming the name of the boy was John was to write it down for the onlookers.