Look on the 3rd screen of ezremaster, "Display settings and mydata.tgz backup". There is a option here that allows you to input a path to a image on your system. Ezremaster will copy the image in to your remastered tinycore.gz and set the appropriate boot code to set the image as the desktop background.
Many thanks for this Brian. I'd missed that entry because I thought it was part of the display modes setup and therefore didn't bother to read it.
Is there a way to include the wallpaper configuration as well as the image? I have a plain wallpaper that by default is rendered as 'Full', meaning that if the aspect ratio of the image is different to that of the target monitor there are borders. Ideally, I'd like to be able to have it come up pre-configured as 'Fill', so that the borders don't appear.