Yes Mike pulled me head out of my rear end with his answer.
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The 120VAC coil would go between battery output and the repeater (either plug or hard wire config on your repeater), all it is doing is not letting the charging current to enter the repeater. If you lose AC Mains, he relay drops out about as fast as the system tries to swap to backup and you never notice anything. It has no effect on normal use, plugged into a wall outlet.
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Kory