I wish every governor who didn't have an ideal induction had your thoughtfulness. Very often this is badly handled because induction isn't planned and is nobody's job.
The important thing is to have an advance plan. The head invites every new governor to call in and gives them a few basic documents (the prospectus, a school building plan, and a list of staff responsibilities).
The chair might telephone them and tell them a bit about the governng body, the main issues, and how the work is managed.
As to work, the best way is to invite new members to attend as many committees as they can for a while to find out what most interests them, making it clear that they can just observe at first but that you hope they will soon be fully involved in all the activities. A new governor might often ask where he or she can look at policies which have been agreed by the governing body. Very rarely are these kept in one place with an indication of when each was last revisited. Old and new governors could benefit from that.