Please describe more fully the support of the Test_Specimen. You show a rod bonded to the bottom. The bottom of the rod has a Harmonic Pressure load which acts along the Y axis and the bottom of the rod also has an elastic support and a Displacement that holds X and Z at 0 and leaves Y Free. In your model, I wonder if the displacement and elastic support on the bottom of the rod accurately represent the setup you have in the lab.
The setup in the lab uses a vibration exciter to excite the bottom of the rod in the Y direction. What is the setting on that vibration exciter? Is that exciter set to provide a Force, Displacement, Velocity or Acceleration amplitude?
My experience is with harmonic testing on a shaker table where the test article is bolted to a fixture which is bolted to the table. The fixture has its first mode far above the highest mode of interest on the test article. Does your test article bolt to another structure?
I have also read about harmonic testing of structures that don't bolt to anything, for example a satellite. Ground testing of satellites might hang the structure from a few springs. A vibration exciter applies a harmonic load at one point on the structure in a single direction using a slender rod called a stinger. Accelerometers pick up the response of the structure at other points.
You were expecting to see a resonance of Mode 8 in the Harmonic Response. Not all modes resonate in the Harmonic Response. Consider a cantilever beam. The first few modes are bending around the low thickness direction, then there is a twisting mode, and later there will be a bending mode around the high thickness direction. If the harmonic load is only normal to the thin direction of the beam, then you will only see the first few bending modes show up. You won't see the twisting mode because there was no load to excite that. If you use two harmonic loads, one on each corner of the tip and they were 180 degrees out of phase, that would excite the twisting mode. In your model, the geometry is symmetric and the load is centered and aligned to the Y axis, so there is nothing to excite Mode 8.