"I'm holding the guitar by the neck around the 12th fret."
The resonances you're looking for will be mostly of two sorts; 'bar type' bending modes, and twisting modes, or combinations of those. You might find it helpful to look up stuff, or do experiments, with simpler systems, such as plain pieces of bar stock or narrow plates, to help get a handle on how these things work. Then it will be easier to make sense of what's happening with your more complicated guitars.
'Bar' type modes will all have stationary 'node' lines or points near the ends of the object. The lowest one will have two of these, with the middle of the thing going 'down' as the ends go 'up'. On a plain rectangular bar the nodes will be about 1/5 of the way in from either end, and there will be a lot of bending going on in between those two node lines. There are 'higher order' modes, with three, four, five, and more nodes as well, although as you go up they get less active. The more node lines there are the closer the two end ones will be to the ends of the bar. All of this depends on the way the mass and stiffness are distributed in the bar.
On something like a solid body guitar the masses of the body, and, to a lesser extent, the headstock, will tend to dominate the 'mass' part of the equations, while most of the bending will take place in the neck. Holding the neck at the 12th fret is going to tend to kill any mode that is moving there, which would almost certainly be the lowest frequency mode, and probably the third mode. The second mode could well have a 'node' at the 12th fret location, or near it. You may well be suppressing modes you want to look at by holding at the 12th fret. OTOH, it's hard to know of any one place that won't suppress something. I've had good luck with acoustics hanging them up by the head, usually with a loop of strong string under the E string tuners. This is close to the node for the lowest order 'bar' mode, and doesn't suppress it too much.
One thing I've observed in tapping on solidbodies is that the lower node lines tend to 'bunch up' near the bridge. The nodes for the first three or so resonant modes all tend to be pretty close to that location. You can think of the nodes as the pivots of a see-saw, and just as it's hard to move a see-saw by pushing at the pivot, so it's hard to drive a mode near the node line. Having the nodes bunch up near the bridge means that they're hard for the strings to drive, so you don't lose energy from the strings at those frequencies.
The places that move a lot between the nodes are the 'antinodes' (yeah: I found the nomenclature confusing too, at first). Putting a pickup on an antinode would mean it was moving with respect to the (you hope) stationary ends of the string. That's going to color the sound. The more I think about it the more complicated it gets.
"I am tapping with the guitar in approximately The same spot each time in relation to the microphone. "
As with the bridge driving, you can't activate a mode by tapping at or near a node line. There's a good 'out' here, though: ALL of the modes will be active at the ends of the guitar. Tapping either at the headstock or the tail should get them all going.
Tapping the guitar will activate all the modes that are active at the spot where you tapped, and that have node lines near where you're holding it. Once it's going it will 'ring' for a while, radiating sound from the more active parts at whatever frequencies they're happy with. The mic will pick up whatever is coming at it. What the mic hears is not related to where it is relative to the tapping point, it's a function of what the guitar is doing. Since all the 'bending' modes will be active at the headstock that would be a good place to pick them up with a mic. It will be moving more there than the more massive lower end of the body will.
I'll note that there's a lot of disagreement about the 'best' way to hold stuff. Many folks, with reason, feel that the most useful way to hold things is the most realistic: support it where you'd be holding the neck and where it would be leaning against your body. That will show you how it's likely to work in use. There's always the issue there that different people hold them differently. I always try to find the most 'free' way to hold them I can, hoping to factor in the holding constraints later.
The important thing is to come up with some sort of test that makes sense from knowing how the thing is likely to behave, and then to do it the same way every time. Once you start down the primrose path of acoustic measurements it's very had to turn back, so think long and hard about this!
