How to find an ethernet cable?
There are digital stud finders that you use with your phone and the hype from their advertising implies you can see anything through anything.  I can't vouch for them but it's worth a look.
There are wire tracers like the toneout boxes the phone company used to use.  There are cheap ones.  The receiver does not need electrical contact, it's meant to work through the wire insulation but I don't know how far through plaster it might work.   Maybe worth a try.
Many VESA mounts are horizontally adjustable on their mounting screws so perhaps you could just drill outside the 10cm band and still get the result you want.