It’s not normal for the CAN wires to be at 12 V.
The CAN wires will be in one of three states. When dormant they will be in the range 2 - 3 V and they will be the same voltage. When active CAN-H will be about 2 V higher than CAN-L. However when you measure with a voltmeter you see the average voltage. CAN data is generally about half active (logic 0) and half dormant (logic 1) so on average the difference between CAN-H and CAN-L will be about 1 V at most, and less if there is little data traffic on the CAN bus.
When the CAN bus goes to sleep and all traffic stops, there will be the same voltage on CAN-H and CAN-L. The various modules go into low power mode and both CAN voltages may change. There is no “correct” voltage at that time, but both must be the same.
The CAN bus going to sleep is not the same as ignition off. Most CAN buses are awake from when the car is unlocked until a few minutes after the engine stops. Some CAN buses stay on for other reasons, such as when an EV is charging.
The other possibility is that those two connections on your car have nothing to do with CAN at all.