That is for some near-DC AM to be converted to AM of the 19-MHz beat frequency. The idea before was that jitter at 19 MHz would turn into a 19-MHz signal from misalignment into the AOM or via any other mechanism that turns jitter->AM (e.g., clipping). This looks like a DC error offset. Then, any low-frequency noise (e.g., slow pointing drift of the steering mirror on the way into the AOM, slow translation of some aperture relative to the beam) causes low-frequency AM of the 19 MHz signal, which looks like a time-varying error signal (noise). AM of the AM.
So, there is some 19 MHz oscillation set up by jitter->clipping or polarization->AM or some gremlin waving his hand steadily across the beam coming out of the laser at 19 MHz. Then, the amplitude envelope of this oscillation is modulated by some low-frequency noise source, and this is what looks like noise when demodulated by the PDH setup.
The question I'm wondering about now has nothing to do with envelope modulation of a 19 MHz signal. Instead, there could be low-frequency pointing noise on the way into the cavity. The cavity reflectivity looks like a real number close to 1 for the sidebands, independent of small angular misalignments. So, any existing 19-MHz signal is not amplitude modulated. The question is: how does this sort of thing become noise? I thought perhaps the eignenmodes of the cavity rotate with respect to each other since the beams are not being injected from symmetric points, and this could cause some relative length change that looks BIG in the gyro signal compared to what a common-mode length change would look like via FSR modulation. This could be why we don't see it in the primary (laser) actuation signal.
I think you raised the possibility that the same low-frequency pointing that causes us to see noise in the DC_TRANS signal could also produce RFAM via clipping or whatever, but in this case we would still see the noise with the cavity obstructed, which we do not.
In terms of a coupling mechanism, I'm wondering about this: If the pointing of the carrier as it goes into the cavity is moving around at low frequency, then that's going to modulate the coupling into the cavity and give us some AM on the reflection PD (I'm not talking about RFAM here, but low frequency AM as the coupling to the cavity wanders around). This then causes the AOM to try to act, so we see noise superimposed on the reflection and transmitted beam.
It seems that whatever the cause, if we are seeing AM at low frequency in the transmitted beam then it is likely that we will also be seeing the exact same signal on our REFL PDs.
EDIT: Zach pointed out to me that there needs to also be some phase shift between the carrier and sidebands for us to get an errors signal. I think that I'm not clear now how we ever expected the RFAM to show up as noise. Where is the phase shift there?