Solder one end to the negative terminal of the battery compartment, and solder the other end to the NC switch connector (3 o'clock position) on the AC socket. When the AC adapter is not plugged in this provides the return path from the circuit board to the batteries' negative terminal. Strip the ends of the red wire the same way.
Now, the batteries are connected into the circuit almost as before. With the AC adapter un plugged, the batteries provide current through the two red leads, and the return path goes up the black lead to the AC socket, through the closed switch, and back to the batteries.
Pics to follow shortly. They are the breather plugs. Batteries produce gas when being charged and it has to vent somewhere otherwise the battery would explode. Possibly. Remove them both. They are the breather plugs. Batteries produce gas when being charged and it has to vent somewhere otherwise the battery would explode. Possibly.
Just curious, the light blue connector that runs along the power cable, you can see the connection just above the negative terminal of the battery, from the OP picture. What exactly is this cable for? Just noticed the other day it was unplugged. Any help is much appreciated!
Possibly. Remove them both. They are the breather plugs. Batteries produce gas when being charged and it has to vent somewhere otherwise the battery would explode. Possibly. Remove them both. It says plug, not plugs? It says plug, not plugs? We can only see half the battery. ETA I see there is only one label. Just remove the single plug.
For your application, choose an adapter with an output voltage that matches the type and number of battery your device uses. You will also need lengths of thin (24 gauge or smaller) wire, one with black insulation and one with red. I cannibalized mine from some left-over four-conductor signal cable.