Green’s Dictionary of Slang

gripper n.3

[the ceremonial handshake of the group]

(Aus.) a Freemason.

[Aus]Canberra Times (ACT) 6 Mar. 17/3: Freemasonry encountered considerable opposition from organised religion, especially the Roman Catholic Church. You had the ‘kneelers’ or the ‘grippers’. The prayers or the handshakers.
[Aus]P. Doyle (con. late 1950s) Amaze Your Friends (2019) 78: ‘Has Laurie joined the grippers?’.