How can I stop a hinge constraint from "snapping back" to default position when disabled?

Might have to fine tune the values in the hinge.

Make sure you don’t have the limits set below the TargetAngle.
You can also play with the Forces and the HingeConstraint.AngularResponsiveness to tweak the settings.

I’ve had issues with hinges bouncing before, but usually when using them on high force items like steering or large Parts with high Density.

And how are you setting the Servo TargetAngle? If the script is constantly trying to change the value it may twitch too.
You could try a wait(.5) or so it doesn’t try to update continously, or check to see if the CurrentAngle is within a 3 or 4 degree range of the TargetAngle so it only updates when it’s outside that range.

It’s moved like this:

if not pressed then
				pressed = true
				repeat
					script.Parent.RotateHorizontalPart.HingeConstraint2.TargetAngle = script.Parent.RotateHorizontalPart.HingeConstraint2.TargetAngle - 0.3
					wait()
				until pressed == false
			end

Maybe add

				repeat
                    if script.Parent.RotateHorizontalPart.HingeConstraint2.CurrentAngle > *whatever value your maximum angle is* then return end
					script.Parent.RotateHorizontalPart.HingeConstraint2.TargetAngle = script.Parent.RotateHorizontalPart.HingeConstraint2.TargetAngle - 0.3
					wait()
				until pressed == false