If your clock is the factory clock , located in the factory location. You Should be able to tilt the steering wheel to it's lowest position and remove the two screews holding the trim around the Instrument cluster (above column, firing upward) and snap the trim panel out carefully. I think the clock in my 97 was just snapped in place, but there could have been some screws..............been almost three years since i did this.
If you use some sort of "Armor All" product on your dash , you may have caused the plastic to weaken and break. whether or not it's snap together or screwed together, brittle weak plastics sometimes seperate quite easily. It is my experienced personal recommendation, that these products that shine and lube your vinyls, not be used. I love Armor All on the tires, but anything else I shy away from.
I do car stereo and electronics R&R and have to replace ( or recomend replacement of ) parts that have these symptoms due to the slickerers.
Sorry for the tangent, but I feel like your description leans toward a weak piece of plastic.
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