It occurs to me that this is a binary search on the alphabet, but could be made into a much more human-compatible format: “Is the letter in the first half of the alphabet?” “Is the letter between A and F?”
If they have vision, you could ask "Which of these two sets is the letter in", where the sets were dynamically generated by predictive software.
On a related note, one character per minute is about the same speed as the first trans-atlantic telegraph cable in 1858.