Great question — answering as the UphillTech team:
All the pedestal basins I have seen have the pedestal free-standing and the basin supported by being bolted into the wall. I would aim to get the basin fixed firmly to the wall. If you cannot find mounting holes, I would try to obtain or fabricate some mounting brackets. If you have a masonry wall, you can use masonry bolts. For a wood-framed wall you need to locate the studs and may need to open up the wall to insert some supporting woodwork to take the weight of the basin (and struggling inebriated guests). If you can identify the make and model of basin, or include photographs of its top and undersides into your question, you are likely to get answers that give more specific assistance....
Full answer by RedGrittyBrick: https://diy.stackexchange.com/a/105792 (CC BY-SA 3.0).
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