May not be the reason for the fluctuations, but why are you measuring an 83MHz signal with a 50MHz bandwidth scope?
Because it's been modded.
On the interference; the radio I was working on was flat on the bench and the scope hooked to a test point made for adjusting max level. After noticing it I backed away from the radio and tried just my hand over the scope, same thing.
I just tried using a signal generator. 50 MHz, -10 dBM into a 50 ohm load on scope. 1m RG58 cable with BNCs.
Using Auto setup it showed 655 mV RMS and my hand has no effect anywhere around the scope. I'm guessing the supplied probe cable doesn't have very good shielding and I was close enough to affect it, abt 6-8 inches, scope connection to top of scope, arm parallel to cable.
Oh well since none of what I do requires absolute measurements it's not a big deal, just strange.