Red is positive (hot) and black is negative. Easy peeezy
Just add to the existing wires to get them outside the case and hook them straight to the battery. Then hook the little solar trickle charger to the battery too, same red/black wires.
Just easier for me to throw away old batteries. As long as they last it's no big issue. I'm there at least once a month filling the feeders anyway. Takes just as long to Replace the regular batteries as it does the rechargeable ones and I don't have to charge or keep up with them.
It's been my experience that one of those rechargeable one will go out and stop the whole device from working then You got to trouble shoot WHICH one is going bad. I tried them and it was a lot of unnecessary trouble.