53 Navigator rocks with auto pilot on

What brand autopilot? Sounds like the rudder sensitivity is set too high.

Regardless of brand, it sounds like a sensitivity issue and you just need to adjust the autopilot.

This. You can usually adjust the sensitivity ( could also be called response) in the menu and should adjust it from time to time for various sea states/conditions.

You guys are good!
I'd have suspected the bilge rats endemic to that particular autopilot model scurrying back and forth between the sensor and the pump as the cause of the rocking.

What brand autopilot do you have? If simrad, put it in auto mode (can be at the dock), then hit the NAV/setup button twice (in rapid succession) you now will go to a menu use the right arrow to scroll down and the knob the adjust, when done just hit auto again..... 2 clicks (one notch on the screen) left will probably fix the issue.....although I adjust the settings all the time on boats I run.....if in the ICW I turn it up.....if in the ocean turn it down.......also if you hit auto twice in rapid succession the autopilot will go in Hi mode and respond faster, if you back the response off this comes in handy as well.

Find a manual and read it, whatever brand it is. You may find some other very useful features you aren't aware it has.

On those Raymarine calls it response, and you just go through the menu button till response pops up and then use the down arrow to adjust it once the screen reads "response and a #". You may have to be in autopilot mode to do this