The Pearl is an outstanding example of extraordinary support of the DIY community through Pass labs - in this case of Wayne Colburn who designed the Pearl.
Since nearly all needed information is contained in
[Wayne Colburn's instructions], you'll find here bits and pieces of informations and discussions that didn't find their way into the excellent pdf just mentioned.
the purpose of the mysterious battery mentioned on the pcb
As
[Wayne himself says], it can replace the D1 Zener diode to form a better 9V reference for the regulator differential amplifier.
How long it lasts, is discussed
[in this post], it seems only 9mA are drawn and if R5 is removed, the battery has to provide only the leakage current of the cap.
