One thing to note is that the website must provide the FavIcon for Safari to view it. If one is not provided by the website, then a generic one will be displayed. Some websites will not have an icon to view. With that said, there are times when Safari will show a generic icon when one is available. I know that your Amazon favorite should show their icon. The problem can be solved by removing the cache for the favorite icons. This will clear all of them, but they should refresh when you tap on them.
As always, before changing system files, make sure you have a backup. This will remove the cache for the icons and allow refreshing.
- Quit Safari
- Go to Finder > Go > Go to Folder
- Paste this into field starting with the "~": ~/Library/Safari/Favicon Cache/
- Drag everything to trash. Should be 1 folder and 4 files.
- Empty Trash
- Open Safari
- Click on each favorite icon and they should now update.