Alrighty boys, if you want to find thumbnails in their highest available quality, I suggest that you use this URL:
Replace the video ID with the ID of the video you want the thumbnail for, and you should be good to go.
I haven't seen a pattern for which videos use the full 1280x720 resolution and which videos use the (mediocre) 480x270 with black bars, but if you come across the latter, I recommend opening up Microsoft Paint and zooming in real close to crop them out. It's weird at first, but it's quick and relatively easy and beats using other things like Google Photos, which are fine in and of themselves, but I want thumbnails uploaded here to be in their highest natural resolution, which other tools like PicResize.com (which I used to use) don't seem to do.
I hope this blog post helps. If you have any questions, just ask in the comments or on my message wall.