“Mogrify” should be called from the directory with the original thumbnails, while the -path parameter is for pointing target directory.
mkdir public_html/images/new-thumbs
cd public_html/images/thumbs
magick mogrify -resize 16x12 -quality 100 -path ../new-thumbs *.jpg
http://www.imagemagick.org/Usage/basics/#mogrify
The last arguments are the list of files, so you can filter by name 1-*.jpg for example.