Looks like you need a NO dry relay in a keypad that runs on 12vac? NO contact goes across "OPEN" on the controller. I assume when this is shorted the gates will open? You could test it out...
Issue would be how to get the gates to shut after a period of time? Unless this is not required? Maybe there is a keypad that counts down on a timer and will then blip a relay that could be wired across "CLOSE"? Otherwise you could manage it using a multifunction timer of some sort.
Have you tried contacting the manufacturer? They may be able to recommend something...
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