I would not use the same 12v terminal as the PAC. Also, you might try a different ground (black wire). The wideband reading should not rapidly cycle up and down like that. You could actually ground the black wire to the ECM case also to see if that helps the problem
The white and brown wires are good. The brown in the analog signal ground, and the ECM case is a good ground for that.
If it continues to do that, we may have to check out the wideband unit.
Eric