Comment by adrian_b
Unless he uses the ticks coming from the two clocks to generate a tick signal whose frequency is the geometric mean of the 2 tick frequencies (possibly by using a weighted mean, when one clock is known to be better than the other), and then displays the time by counting the ticks from the synthetic tick signal.
This is how the redefinition of the second will work, by using many different kinds of optical clocks, instead of the single cesium-based microwave clock that is used now.
In fact, today the big laboratories have many atomic clocks, whose clock frequencies are averaged to compute the time, even when the clocks are of the same kind. The international atomic time, TAI, is computed by averaging the clocks of all important laboratories.
I wonder why they use the geometric mean. Are the clocks expected to have spurious noisy ticks?