Been poking around and think I got it. (I got it working in Mojave. Haven't tried a reboot, but it survives restarting Finder).
Before making the link (as described above), you need to change the original Trash folder's icon:
Trash is a hidden folder (named .Trash) you can get to it by going into Finder > Go > Go to Folder... (cmd-shift-G) and go to:
~/.Trash
This will open the .Trash folder in Finder, and using Columns View Finder > View > as Columns (cmd-3) you can chose the grayish/hidden .Trash folder and use Finder > File > Get info (cmd-I).
Now you can change the icon, with a .icns file (it might work with any square image file, but I only succeeded with an icns file.) You can make icns files from any (square) image - with dimentions 512 x 512 px (and perhaps 1024 x 1024), but if you just want the old can (like the one underneath),
you can download an icns file from here.
To change the icon of .Trash drag the .icns file to the little folder in the top left corner of the Trash info window (NOT the tiny one in the top bar, NOR the larger one in the Preview section). Once it 'takes' all three of those should change.
NOW, you may open Terminal and type
ln -s ~/.Trash ~/Desktop/Trash
And you should get an Alias with the right icon onto the Desktop. Every thing you drag and drop into that alias ends up in the trash.
NOTE: This approach does not make the Trash icon dynamic (you cannot see if it's empty or full). Nor does it change the Trash icon in the Dock. Doing that requires a bit more stuff, including some scripting and would in all likelyhood also violate the System Integrity Protection (csrutil) as
@mfram points out.
