For the period 1500 AD to 2100 AD I obtained annual locations of the barycentre relative to the Sun and took only the absolute value of the Z axis component of the deviation from the Solar equator of the barycentre. The absolute value is taken because it is not important whether the displacement is N or S, just by how much.

Using a spreadsheet FFT (Fast Fourier Transform) for 512 years starting in 1500 AD I calculated and plotted the FFT of the absolute N-S displacement of the barycentre relative to the Sun.



You can see that when the absolute value of the displacement is used, the 11.86 year period of Jupiter no longer dominates the spectrum, but the planet pairs of frequencies (either + or -) make the strongest components of the spectrum. The J-N component is exactly at the true sunspot cycle peak period. Other periods found here in the range 8 to 14 years are also found in the sunspot cycle.