Why do ELT panel switches have batteries in them?
The battery in the remote switch like the ACK 406 ELTs powers the LED in the remote (the ACK ELT has a separate battery for its alarm buzzer).  On some ELTs the remote's battery may also power the alarm buzzer (the one that warns you the ELT is broadcasting in case you missed the red LED) that you install near the remote (my old AmeriKing 406, now a desk paperweight on account of AmeriKing's TSO certification fiasco, had the same remote that ACK uses and it appeared to power the both the LED in the remote and the little alarm buzzer, because the alarm was wired directly into the remote with no other apparent source of power).
Some units like the ARTEX ME406 don't have a battery for the remote switch (the ARTEX unit's buzzer has its own battery), and on those units you have to either connect a remote switch power source wire to the airplane's electrical system, or if in a no-electrics airplane, you have to cobble together a separate battery power supply to power the remote's LED.
I couldn't find an engineering specification with the information, but I dimly recall that all this is because the ELT's internal battery can't have a potential load device, like a light or speaker (buzzer) connected, that could drain the internal battery if the external light/buzzer shorts out, so they require their own power sources.