We just had new counters installed in our home. The guys field-measuring had no way of knowing that behind the existing laminate backsplash the plaster had been cut away. When the new counters were installed we were left with a gap at one location. We had the wall patched to make up some of the difference, but we're still left with 1/4"-3/4" gap (1860's house, the walls are not exactly straight).
We plan to tile the wall behind which will make up for part of it but obviously in the larger areas we'll still have an issue.

Of course it occurs on a 5-6 foot piece of wall directly behind the sink, so we'll want to be cautious of making the seal watertight.

Any ideas to properly fill and seal the gap? Thanks