What autopilot is installed, and with AP off did you have Force Trim on or off?
Also, are there any modification to the collective head from a standard 412EP?
This sounds a bit like a control response to the aircraft movement causing the oscillation. With the AP turned on, the control in question no longer moves due to aircraft movement so the oscillation stops.
Although you said it was a vertical oscillation, I think it could have been either a heave oscillation or a pitch oscillation. Either may feel as a vertical from the cockpit. A modification that adds mass to the control head, or control frictions being too low could lead to this.
A little bit of theory, but mostly a wild guess.
Great job in bringing it down, keeping everyone safe!!