A network of clocks on the moon could work in concert to inform the new lunar time scale, just as atomic clocks do for UTC on Earth.
Presumably some clocks would have to be on the surface of Luna facing Earth/Terra, and some clocks on the side facing away, so that the gravity well of the planet could be averaged out.
And if we're going to go through the trouble/expense of sending some gear, it might be useful to pack multiple instruments: if timekeeping is a long-term need, another long-term instrument could perhaps be a seismograph to measure for possible 'moonquakes'. Multiple clocks could mean multiple seismographs for better triangulation of events.
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Presumably some clocks would have to be on the surface of Luna facing Earth/Terra, and some clocks on the side facing away, so that the gravity well of the planet could be averaged out.
And if we're going to go through the trouble/expense of sending some gear, it might be useful to pack multiple instruments: if timekeeping is a long-term need, another long-term instrument could perhaps be a seismograph to measure for possible 'moonquakes'. Multiple clocks could mean multiple seismographs for better triangulation of events.