The only thing that battery does, by the way, is light up the LED. I spent some time at the last annual diagnosing a problem tehre. That remove is pathetically stupid. The phone jack (and make sure you get the right pin configuration, phone wires can be installed one of two ways and it makes a difference) on the thing has a ground, a wire to each of the the the two buttons (which just short to ground when you push them), and the signal (grounded when active) for that the ELT is transmitting). The battery just goes in series with the LED between ground and the signal line.
If you have the wrong "polarity" on the connector, the ELT triggers as soon as the remote is plugged in.