My 1935 house has the same "problem." On every ceiling you can see the 16"x4' seams. It is also like that on all of the upstairs walls and many of the downstairs walls. We did a kitchen remodel a couple of years ago and it was interesting to see that the some of the walls were plaster and lath and some were either the gypsom or beaverboard described by others. I thought maybe they splurged for plaster and the living and dining rooms, but there didn't seem to be much method to the madness. I'm not sure whether its the plaster coat or the boards themselves but they are literally rock solid. I have to use a drill to hang anything, and many times the drill bits break. The grooves don't bother me as much as the peeling paint. In a few of the seams on the ceilings the paint literally falls right off. I'm not sure if I should blame it on a bad paint job or the materials in the ceilings. I also have the faux-tile that ken tn speaks of. It went all around the kitchen from the floor until about five feet up. It was in the bathroom and the half bath as well. In the kitchen the previous owner just plastered over it, but you can still see the pattern in places. I'm not sure if it was a stamp or something premade, but it is definitely not 4" ceramic tile. I don't know that the finish or paint colors have made much of a difference. It's very visible on the flat white ceilings and very visible on the various colors of satin walls. I did find many of the same old colors, lots of teal, green and coral around too.

I don't like the LED idea. I would suggest a piece of wood molding, maybe 1" or more, painted to match the tile color. If you caulk carefully where the molding overlaps the wavy tile -- so that the small gaps are filled in -- it will look just fine after you paint it.

@ beesneeds...sadly the 'tile install' has NOTHING to do with wall structure. Sigh...I know. A 'tiling professional' is a specialized subcontractor (and is expensive...which is why MANY general contractors do NOT use them...they loose money because they have to pay TOP DOLLAR for a tile pro...just sayin'). A tile setter (in a high-end company) comes in when the walls have been dealt with. The tile setter will add the water proofing to walls and shower pans, etc. S/he will install the crack prevention membranes like Ditra or Schlutter. They then spread their thin-set and start setting their tile. Before they drop in a single tile they would have done an hour or so of measuring and calculating to ensure the tiles are centred properly and that corners do not have 'slivers' and everything else that goes into making tiles look 'good'. They will also sort their tiles (again...can be an hour worth of work all total) and work from groups that are in the same size range, etc. All of this 'precision' costs a contractor MONEY. That means a contractor will often 'cheap out' and use one of their 'guys' (who will rip out walls, pound nails, run to the coffee shop for lunch...etc) to do the tile work. The General Contractor (who is probably not the tile setter pro) is responsible for the stud work and the cement board and the taping and the mudding of said board. To fur out walls and to make them plumb and square can take a day worth of work...and that can be fiddly. Remember: time is money to these guys. The faster they get the work done, the more money they make. If they have to lose a day and a half (1 day for the walls + 4 hours for a tile setter to do all the sorting and the math) the GC will lose close to $1000. And that is pure profit. The tile pro comes in and takes over when the walls are up (studs covered) and then does the work required to get tiles to work as a water proof surface. If the GC is also the 'tiler' (not trained in tile work), you get issues like this. We see this ALL the time.

"Zellige should not use a grout joint (should be butt jointed). Wedge spacers can be used to allow for variation in the butted tiles. Minimal maintenance is required on Zellige tiles. Mild soaps or neutral cleaners should be sufficient for most cleaning." Gotta be honest. No it doesn't look great. HOWEVER. You are not running a sauna. It's too much darn tile for ANY kitchen , it's overkill in any tile. It was beyond ambitious in this tile. Re do the back splash, perhaps with a different installer, and btw.......we know not how plumb your walls. The window wall? Drywall. Or bottom of cabinet height at most. Sorry.......but the entire concept of tile, protective and decorative - has gone beyond the pale. Yes, I well realize not what you asked : )