My 1981 M20K model has developed a slow pitch oscillation, new to my 30 years with this plane.

In level flight in the teens, power 65%-70%, carefully trimmed, it will gently start to pitch up and I need to gently push, followed by a slow pitch down and I need to pull gently. It's quite determined to do this every 5-10 seconds.
If the KFC200 A/P is on in ALT mode, it will adjust pitch trim to stay level, every 5 seconds or so.
The yoke, its panel guide, and the elevators are mechanically smooth and solidly connected (ground test).

What could this be? I think it's a phugoid oscillation, but what's inducing it?

This is a  Peter Garrison kind of question...