I put a cabinet up on tiles on plasterboard. Didn't fall down. But is wasn't 13kgs ....
My non-expert option: Plasterboard is pretty solid material, but crumbly. Tiles are rock hard. Together they should be able to take a lot of weight as the adhesive and grout will bond it all together like one solid stone wall.
I think John's rail idea would be sensible - spread the load.
once you have drilled the first hole, you can poke a Special Tool through it, and feel, sideways, each way, until it hits a stud. Mark that distance on the wall and drill just beyond it.
I sell this Special Tool for £50 plus p&p, or you can make your own by unravelling a coathanger and bending it into a shallow curve.
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