I am sure there were others with similar problems, but often their solution (if ever written down) is buried is many other info and I found it hard to find the solution to my problem:
When I tilted down or up (pitch), the roll axis and the pan (yaw) axis started to move also. This was with the RC-joystick control as that is what I need for this (cable-cam) application

After a long search I found 1 answer that made sense; the camera IMU is possibly not perfectly aligned with the camera-plate.
So that was the first thing to address and indeed, that IMU was a) not completely in line and b) due to the construction with a cable to the little board going through the hollow tilt-axis, it could also slightly move when tilted to extreme angles (more than 80 degrees).

After that was fixed (literally), there was still some roll and yaw movement when tilting down. It took a while to find the right options in the Hardware-tab,:" Misalignment correction: angle of rotation over XYZ axis " at the bottom of that tab.

First I tried the AUTO function, but that did not make much better of different.
I found it was better to try manually, by placing numbers in 1 axis per time, and see what changes. What I suspect is that the 3 positions that are the X, Y and Z axis, might be not always XYZ, depending on actual mechanical construction of the IMU in the gimbal.

This way I found the nearly perfect numbers to make the gimbal/camera point straight down, without moving the pan or roll axis.

It is best to start with big numbers, like 10, so you can see which way the axis moves. Then reduce those numbers, 1 axis at a time, to get the best result.

This was for a small gimbal , the H2 from Dactylcam, (discontinued already) but I suspect this principle goes for most gimbals.