Unlike around a tub, there doesn't have to be a gap above a counter. There are silicone adhesives that caulk and attach to the wall and have moldicide in them. Just press on the wall and down, wipe off excess, and run a tiny tool along the edge when dry. The handle end of tweezers works, or something even smaller, like a dull pencil or retracted ballpoint pen.

Thanks for the advice.

If the backsplash is in, use masking tape to make a fine line at the junction, use clear silicone-small tube, squeeze a small bead, smooth, let set a couple of minutes and remove the tape. After it sets, use an exacto knife to carefully remove the surface caulk.