Hi @jfordham,
Thank you for your question about sealing the gap below your tiles.
With the gap being as wide as it is, using an aluminium flat bar or aluminium angle to cover the gap is a good option.
If you want a more professional-looking finish, you could clean up the bottom edge of the tiles and install a tile trim like this QEP 8mm x 2.5m Silver Mosaic Tile Trim or use a cover trim like this QEP 28mm x 2.5m Duracover Silver Tile Trim.
Being behind a sink, you're going to want to use a silicone product such as SikaSeal Kitchen And Bathroom Silicone Sealant. Unfortunately, these products are not paintable, but there is a variety of colours you can choose from. White is a good option against tiles like this.
If you use a trim or aluminium product, the silicone can be used to glue them in place, before applying a thin bead to the top and bottom edges to stop water getting in behind.
Check out How To Silicone a Gap for some guidance.
Let me know what you think and if you have any further questions, please don't hesitate to ask.
Jacob
