Problem solved! It turned out that in copying Mail from the Applications folder on my boot partition to the other partition, some files failed to be copied. I had deleted the original application, so those files were nowhere on my hard drive. When I control-clicked on Mail and looked in the Resources folder (in Contents), the .tiff files up to first-lettter "s" were there, but when I compared to Mail on a different Mac I saw a bunch of files that came later in the alphabet, including a bunch of "TB_..." tiff files - these evidently were the ToolBar icons. When I copied them from the other Mac and restarted Mail, my missing icons were back.
This leaves the following mystery. Before I did the above I tried reinstalling Mail onto my boot partition from the Tiger install DVD. For some reason the newly installed version was still lacking those icons. Is this a surprise to anyone else? Why wouldn't installing an application install all of its contents?