For the plumb bob method in general, the pointer will point down through the fuselage to the three-dimensional CG, which is located somewhere in the interior of the model. But all you can go by is the visible point on the fuselage exterior. Therefore, for reasonable precision, you want the model to be straight & level. In the sling variation I use (without the dowel and twisting cord), I just slip the sling a little forward or back as needed to have the model hanging level in pitch and roll. With the Vanessa rig, I understand this function is performed by rolling the cord one way or t'other on the dowel.

Aerodynamic neutral point and CG are typically different, although they may coincide. If they're different, you make it up with adjusting wing incidence or decalage or control surface trim. What we call 'the CG' can be understood two ways. Any mass has its natural, physical CG. In setting up your model, you decide where you want that natural CG to be, and distribute your movable masses (battery, servos, ballast, etc.) to make your 'design CG' come out where you want it--let's say at 33% of mean aerodynamic chord, laterally centered on the fuselage. The aerodynamic neutral may be forward or aft of where you arbitrarily set your design CG, which you'll discover when you do your trim flight. So you test fly, trim surfaces for straight & level, and after observing and feeling how the model is flying, you nudge the CG to take out the trim, until you like how it flies. No more measuring, no more calculating, no more plumb bob, just fly it and change little things (wood prop or composite, heavy or light spinner, shift the battery, etc.) until you like the result. So the design CG is a first approximation, chosen for the purpose of positioning the heavy components for which you have some choice as to where to put them.

The hanging and plumb bobbing is only done once, and I do it with every component installed, with the usual exception of rudder servo(s) and battery. These I simply slide around (maybe with a little patch of double tape to keep them from rolling off a rounded surface), and the new configuration will naturally swing its new CG under the pointer. When the pointer comes to rest at the spot I have marked, I then figure out how to do the final installation of the variable components.

The old way I used to do it was to just put everything where the plans said, and then add lead to bring the balance to the manual's specifications (which are reliably nose-heavy, usually at 25% of MAC). The way I do it now lets me use necessary components instead of ballast, saving who knows how many ounces and even pounds of lead on a large model. So the possibilities for conserving lightness can be very considerable. If you're lucky, and the trial CG comes out very close without the battery, you can choose a lighter LiPo or whatever and put it right at or very close to the CG. If you're way off, you can make up a lot of balance with a heavier nicad and put it out on the engine mount beams or way back in the tail or anywhere in between. Sometimes this means cutting in a hatch to mount and remove the battery, which I've done, and seen it done on other people's pattern models.