______ in a geodetic leveling instrument exists when the plane of the image and the plane of the cross-hairs do NOT coincide, and should be eliminated by _____ the objective, eyepiece, or both.

The phenomenon being described in the question refers to an optical issue where the image observed through a leveling instrument does not align properly with the cross-hairs. This misalignment is known as parallax. In geodetic leveling, parallax must be eliminated to ensure accurate readings.

When the plane of the image does not coincide with the plane of the cross-hairs, it can lead to measurement errors. To resolve this issue, the user should refocus either the objective lens, the eyepiece, or both. Refocusing adjusts the optical system so that the image and the cross-hairs are in the same plane, thus eliminating the parallax effect.

The choice associated with parallax and refocusing captures the actions required to mitigate this optical error in the leveling instrument. Other combinations might mention non-collimation or changing, but they do not directly align with the established terms used in optical geodesy for addressing this specific issue. Refocusing is the correct term here, elaborating precisely on the necessary correction method for the condition described.