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Camera-robot calibration reference point

I have a KUKA iiwa R800 and I need to perform hand-eye calibration with a fixed, externally-mounted camera. I've found a number of packages that help me do that:

Both of these packages involve affixing a calibration target to the robot end-effector. My question is the following:

Wouldn't this simply calibrate the camera to the target's frame? I need to calibrate the camera to the base frame. Am I correct that I would need to somehow come up with the target-to-base frame transform? If so, wouldn't this be dependent on the shape/mount of the calibration target?