There are several XML attributes used when interacting with certain parts via mouse or touch inputs. Most parts that can use these have reasonable default values and work right out of the box. Cylinder grips however are a very generic part and have no default values for interaction, as they depend on the configuration of the control base they are connected to.

These XML attributes apply to PosedGrip modifiers:
screenXPositionAxisMap - Vector3
screenYPositionAxisMap - Vector3
screenXRotationAxisMap - Vector3
screenYRotationAxisMap - Vector3
screenAxisSize - Vector2
screenAxisDeadzone - Vector2

The axis map attributes are comma separated float values, typically ranging from zero to one that define a mask for inputs that are applied to the associated ControlBase modifier.

An easier way to look at it though is an AxisMap attribute value should match its associated ControlBase axis value. If a ControlBase is using a RotationAxis, match its axis value with a screenXRotationAxisMap or screenYRotationAxisMap. If a ControlBase is using a PositionAxis, match its axis value with a screenXPositionAxisMap or screenYPositionAxisMap.

Gator Example with unrelated XML removed:

<Part id="1190" partType="ControlBase-Joystick-1">
<ControlBase.State>
<RotationAxis axis="1,0,0" input="Throttle"/>
</ControlBase.State>
</Part>
<Part id="1193" partType="Grip-Test-1">
<PosedGrip.State screenYRotationAxisMap="1,0,0" tooltip="Collective" />
</Part>

In the above example, the control base on the collective controlling the throttle uses a RotationAxis on axis "1,0,0". To interact with that, we can use a screenXRotationAxisMap or a screenYRotationAxisMap with a value of "1,0,0" to match the ControlBase rotation axis.

The screenAxisSize is 2 comma separated floating point values that represent a percentage of screen space that define the 0 to 1 (or -1) range of the axis. The screenAxisDeadzone is the same thing, only it defines the deadzone for the axis.

Take screenAxisSize="0.2,0.4" with a screen resolution of 1000x1000 for example... This means that when you click on the part to interact with it, then drag the part left (for an X screen axis) or down (for a Y screen axis), the input changes from zero to -0.5 at 100 pixels and to -1 at 200 pixels. Likewise, dragging it up or right, it would reach an input of 0.5 at 200 pixels and 1.0 at 400 pixels.