@Tim Trittin I'm not sure if it will be as simple as it seems - I believe if the battery goes dead you lose the whole mag/Piezo circuit, not just the Piezo. This is important because if you put a switch on the Piezo pickup wire, it essentially opens the circuit and cuts the electricity, which then cuts the magnetic pickup too. This is my understanding, hopefully someone can confirm, or I can once I get my guitar back together.
If you look at the pics of the circuit board, there are two sets of pads for the Piezo and Mag pickups to connect to, but only one pad set is used for each. For the Core guitars that have an on/off switch, both pads are used. So I assume there is some circuitry that keeps the battery connected but bypasses the pickup.
IDK what happens if you try to wire the two circuits together, separated by a switch - maybe there is some popping when you go between the buffered, low impedance Piezo and the high impedance magnetic circuits.
Again, this is my strong hunch but I'm not 100% certain. I'm not far from reassembling the guitar, I just have to get comfortable with hammering or pressing in a bridge post bushing before I continue.