The term κωφός, according to William Arndt, Frederick W. Danker, and Walter Bauer in A Greek-English Lexicon of the New Testament and Other Early Christian Literature (Chicago: University of Chicago Press, 2000), can mean either just mute, just deaf, or both, and gives numerous references for each to other Greek texts supporting the various usages.
So the term has flexibility.
It is clear that Zechariah was at least mute, as to whether he was also deaf, two things point to that being unlikely:
- After he was struck mute, he apparently continued in his priestly duties until his time was over, so v.23 (NKJV):
So it was, as soon as the days of his service were completed, that he
departed to his own house.
It is unlikely he could have continued in that capacity at all if he had also been struck deaf.
- The term used for "made signs" is the imperfect active indicative third person plural of ἐννεύω, which Arndt, et. al. state means "to signify by bodily movement, nod, make signs." It is a very imprecise term, as it could simply be that after Elizabeth made her statement at the child's circumcision that he would be called "John," they simply looked with raised eyebrows (or some other bodily gesture) to Zechariah to confirm she was speaking for him correctly. He chose not to just give whatever affirmative head nod may have been common in his time for "yes," but to write it out.
The point here is that the "signs" were not necessarily some type of sign language to communicate to a deaf person (if such really existed then...?), but rather merely some type of bodily gesture by which they sought affirmation that he agreed with Elizabeth's statement, quite possibly as they were making the verbal statement in v.61 "There is no one among your relatives who is called by this name" (NKJV). So the word does not necessarily imply he was deaf.
Without point #1, I think it would be hard to prove whether or not deafness was intended as part of Zechariah's affliction, since the term is so flexible and the v.62 statement could lead that way. But if one lost both hearing and speech at once, then I think it would be impossible for one to function in the priestly duties he did continue with. The trauma alone would be monumental, not to mention the communication issues with the other temple personnel (which were no doubt hampered enough with his speech issue).