Your Gmail templates are stored in your Google Drive folder called Gmail Templates.

You can edit these templates directly from your Google Drive – there is no need to open Gmail composer (as described here)

Here is how to do it:

1. Go to your Google Drive
2. Click on “My Drive” and open Gmail Templates folder:
   
3. Right-click on the template you want to edit. Select Open with -> Edit HTML:
   
4. The editor will open in a new browser tab:
   
5. When you are done with editing click on Save and Close

Here is a short video describing the above steps: