The ‘stopped clock’ is of course a major trope of crime fiction, though apparently has featured in some real cases - but mainly in relation to mechanical wristwatches back in the day.
Given that the photo of the clock dates from eight years after CL’s disappearance, the most likely explanation is that the battery ran out and the clock stopped at that time by pure coincidence. Another option might be that someone with access to the house (before or after CL’s disappearance) deliberately stopped the clock and set it to that time for reasons of their own - and it may of course be that in highlighting the 9.37 coincidence I am unwittingly furthering their intentions. [ETA - though of course the battery may have simply been removed to prevent corrosion and the time again purely coincidental]
But this type of wall clock usually has a mechanism with an open battery compartment (see photos below) - depending on how snugly it sits on the wall, there is a also small chance that a sharp blow to the front of the clock (such as might occur in the course of a violent struggle) could dislodge the battery sufficiently to stop the clock.
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