1-New variable and new trigger
One of the easiest ways to distinguish a 404 page from a normal page in your analytics reports is the Page Title
You must first create a user-defined variable in Google Tag Manager: Page Title.
To do this, log into your Google Tag Manager account, go to Variables and create a new one with the following parameters:
Title - Javascript - Page Title
Type - Javascript
Name of the global variable - document.title
This variable will return the value of the title of the page the visitor is currently on.
Then, you have to create a trigger that is triggered when the page title contains "Page not found". In your case, the title may be different, so use whatever works best for your website.
In your Google Tag Manager account, go to Triggers and create a trigger with the following settings:
Important - this trigger is case sensitive. So, if your 404 page title is Page Not Found, then the Page Not Found trigger will not work because Not Found ≠ not found.
Or you can simply use this trigger condition instead:
2-New Tag
The second step is to create a Tag, for this go to Tags and create a new tag:
Title - GA Event - 404 Error
Type - Universal Analytics
Enter the Tracking ID (if you still haven't done it, I recommend you to add the Google Analytics Tracking ID as a constant variable. This will save you a lot of time and trouble in the long run).
Tracking type - Event
Event category - 404 error
Event Action - {{Page URL}}. Each time this event is triggered, Google Tag Manager dynamically fills in the page URL (full web address) as the event action. This way, you will see which URLs get the most 404 error occurrences.
You can also use {{Page Path}} instead of {{Page URL}}, if you wish. If your web project spans multiple domains and all data is visible in a single Google Analytics account, you should definitely use {{Page URL}} as an action.
Event without interaction - true
Link the Pageview - 404 Error trigger created earlier to this Universal Analytics tag.
Click Save, enable Preview and Debug mode and check if the tag ONLY fires when it is supposed to.