I believe I just found some irregularities with this module. I've tried using it this way:
When I try to read the value back I am consistently being asked for password. Same goes for ACCESSIBLE_ALWAYS, ACCESSIBLE_WHEN_UNLOCKED, ACCESSIBLE_WHEN_UNLOCKED_THIS_DEVICE_ONLY, ACCESSIBLE_ALWAYS_THIS_DEVICE_ONLY.
According to https://developer.apple.com/reference/security/keychain_services/keychain_item_accessibility_constants I should not be asked the password... Tested with TouchID module v 2.1.0 Ti.SDK 6.0.1 GA on iPhone 7 os 10.2.
Please reopen the ticket.