We have two bedrooms in which each has an individual sink BUT.. the back on both, (where the mirror is, under the sink and back of the cabinet), is connected.... IOW both sinks, even though in separate rooms, have the same plumbing to the separate valves.

Since it's the back wall of the cabinet it's solid wood.... drilled holes allow the tubing thru. So no, no sheetrock... yeah, sheetrock I could do with a butter knife. I have a saw that could cut thru it but the risk of going too far would be high... also the risk of puncturing another hole in the plumbing. It required a shallow cut. - JamesJM