Where do views/panels get their source html code I'm working on a few sites that use views/views-ui/panels to display content.

The entry points of the templates are located in the active theme directory
for example 1 view with settings of Format: Bootstrap Thumbnails renders the file views-bootstrap-thumbnail-plugin-style--title.tpl.php

But inside here is only a loop which prints out $rows of large html strings.

This is the same for most sections which simply print $variable.

I've tried using xdebug and followed the stacktrace but get completely lost in the nested functions, and can't keep up with the large unorganised $this variable.

I've also tried root directory searches of strings from the HTML which only finds html in the cache.

Where do views/panels get their source html that's inserted into $row $content etc.. ?
It will depend on the contents of the panel or view display as to the actual content to be displayed.  For example a panel/view might contain a node, in which case a specific display mode would be used dependant on the output settings.  Using your example whichever module provides the Format: Bootstrap Thumbnails is likely to be the candidate which can either be further overridden with a different template, or with an appropriate hook_theme.