Here is a screencast of my attempt to find the (default) gadget which loads the Teahouse script (on Chrome):
https://en.wikipedia.org/wiki/MediaWiki:Gadget-teahouse.js

Works for me.

The gadget is marked as default, but it was not check on Special:Preferences for me. Are you sure, that it is loaded? Type "mw.loader.getState( 'ext.gadget.teahouse' );" into the console, if you get ready it is loaded, if you get registered, it is not active for you.

Yes, since I was logged out, the module was loaded:

mw.loader.getState( 'ext.gadget.teahouse' );
"ready"

That gadget is just an example anyway, because it happens for others as well.

I also restored my preferences to default explicitly for testing this (but noticed the problem earlier, when I had many more gadgets/scripts running).

Hm.. It seems only happens after the page is loaded at least two times... o.O

This is probably caused by the gadget's script being cached in localStorage, and executed from there (basically using eval(), which tends to hide it in debuggers). Try doing mw.loader.store.clear() in the console and reloading the page, or using debug mode (?debug=1 in the URL).

Thanks! The search works after mw.loader.store.clear() + reload, but that will not be so useful to debug intermittent bugs. They might not happen in the next page load.
Also, debug mode is not reliable, because some errors are not reproducible in debug mode =/
T64605: ResourceLoader: Debug mode should not execute scripts in the global scope

I'm not sure what are clear criteria to judge whether this task is "resolved" at some point, especially given the provided input
@He7d3r: Could you clarify?

If there is an easy way to find, just after a JS error occurs in production mode (i.e. no debug mode, and without reloading the page), which risks not causing the error again), which part of which JS code contains a given string.

PS: I should add that I'm subscribed to the error events (by means of mw.trackSubscribe( 'global.error', function ( topic, err ) {...}). This way, I can notice when these errors happen, even if my console is not open.