To commincate the problem better I will concentrate on this simplified representation.
I will refer to the blue object as the Yaw, which will rotate around the Z axis and to the red object as the Pitch which will rotate around the X axis.
When rotating the Yaw object, the Pitch object should follow as if it was connected. When rotating the Pitch object, the Yaw object will be unaffected.
Add two bone at the position, where the rotations should occur. Parent the Pitch bone to the Yaw bone, this way it moves as a child when rotating the Yaw bone.
Add a control bone. The user will only interact with this single bone, we can hide the other bones later. Position and scale it at convenient values, so that we can easily grab and manipulate later. Lock its Z axis, and set its rotation order to ZXY.
Add a Copy Rotation constraint to the Yaw bone. Select the ControlBone as the target bone. Choose Local space for both inputs. Finally, make sure only the Y option is checked, since we only want the bone to copy the rotation for it's local Y. (If we had oriented the bone differently than shown in the second image, this option would have to be selected accordingly.)
Add the same constraint for the Pitch bone. Use the same settings except for the axis. Only select the X axis for this bone.
As a result, when you select the control bone and rotate it in the viewport, the constrained bones will only copy the rotations which we selected. The telescopes orientation can be controled with a single bone now.