This looks like non-linearity producing the 8MHz response.
Does this make sense? Is this to be expected for the SSA3021X?
As is generally known, the first component in a spectrum analyzer after DC block (optional), input attenuator and pre-selector (optional) is the mixer.
Mixers are a non-linear devices by nature, so they will indeed generate harmonics of the input signal.
The CP of the SSA3kX is a bit low at -5dBm and that means that accurate amplitude measurements are possible up to some -10dBm at the mixer input, but for distortion measurements the signal levels need to be much lower than that.
When in doubt, it's always a good idea to have a look at the datasheet:
Second harmonic distortion: fc>50 MHz, mixer level -30dBm, attenuation = 0 dB, preamp off, 20°C to 30°C , typ. -65 dBc
For your specific test with a signal level of 0dBm and 20dB internal attenuation this means you need another 10dB attenuation to get a mixer input level of -30dBm and then you can expect a 2nd harmonic distortion of -65dBc typical.
Looks like your device is a lot better than that, even though your signal frequency was way below the specified range of >50MHz.