grounding plane high frequency circuits
If you connect the scopes probe tip to the exact same point the ground clip is attached to, then the reading MUST be zero voltage AC and DC.
If you are measuring anything other than zero, then you have inductive coupling into the scope leads. This could be because you have too long a wire on the ground clip or the scope cable has a broken shield, or the scope probe itself has in adequate shielding.
Try this experiment. Connect up your scope to the ground trace and observe the waveform. Now, without moving the scope's probe connection, reposition the scope cable. Run your hand along the cable, stand on one foot, wave your free hand in the air, take a step backward, away from your circuit, etc. If any of these physical things changes the signal amplitude, then external coupling is corrupting your measurements.
For noise analysis, we usually have to use an active FET probe. This elminates all influences of the coaxial cable between the probe and the scope. Also, my boss considers any ground wire connection longer than 1 inch as a poor ground. The grounds must be very short.
Can the 12MHZ signal be seen amplified in the output of the amplifer buffering the gyro? It is not uncommon for the inputs to look nasty. This is mainly due to injected noise from the scope probe itself. If you have a dual trace scope, attach probes to both the input and output of the gyro amplifier. Watch the waveform at the output, it it cleans up when you disconnect the probe from the input, you know that your scope connection to the input is upsetting the circuit.