Two physical grounds??

The problem is only if some voltage difference between the two grounds.
With the rods so close, i doubt you will have a voltage differential.

If possible it would be best to tie the 2 ground rods together. Elizabeth is right about the possible difference in ground potentials. Otherwise in a worst case scenario IF you had a direct hit by lighting the voltage would jump from 1 ground to another. This happened to an old customer in Texas and the concrete floor between the 2 ground rods exploded. Again they took a direct lightning hit.

Try running a #14 awg to the outlet that your power conditioner is using, to a cold water pipe and clamp off to that. Swap out the old two wire outlet to a new three wire grounded outlet. The NEC allows for this and will provide an equipment grounding conductor for your conditioner. You can also run an addition wire to a driven ground rod if you would like. Don’t have any idea where the neutral (grounded conduction) receives it’s ground reference and might result in noisy ground loop, if so you can buy various products to combat that and the conditioner is much safer with the grounded outlet. Good luck. T. J.