So, here is the jsfiddle:
Here is the link to the plugin (featherlight lightbox)
The issue is that using the default targetAttr (which is data-featherligh
$('selector').featherlight() (or using data-featherlight) is for binding, like $('selector').click( function() {...} ).
$.featherlight(...) is for triggering, like $('selector').click()
So, bind on click and trigger, or bind via $('...').featherlight, but don't bind on click and then bind in that handler, like you're doing now.
featherlight() has a build-in click trigger so you just need to call the plugin directly:
jQuery('.something_else').featherlight({
targetAttr: 'data-single',
});
see: https://jsfiddle.net/5e9e2k6y/9/