You are correct in creating the texture image with the tile:
format. Simply apply -negate option to invert the result. After which, a simple compose & composite command to apply the "Color Dodge" effect to any given image. See the Compose Examples article.
convert \( -size 1056x576 tile:Castillo_001.gif -negate \) \
source_image.jpg -compose Lighten -composite out_image.jpg