Only html can be embedded in an email. All other forms of report, (pdf, rtf, xlsx, etc) have to be attachments and that is one more click to get to the report. (My wrist honestly wouldn't put up with it)
But I think I solved the issue. I changed the location of the image to C:\Program Data\Quest Software and had the TIC admin copy the image to that directory on the TIC server. So the file is there when the report is made. This seems to work. It appears that this image is a dependent file at run time but does get embedded if the file can be found on the TIC Server.
I found another irritating bug while doing this. I have about 30 reports at this point and needed to edit all of the tdr files. So I thought I would use the TIC "Edit Script" option. When you do this it saves a copy of the script to C:\Users\xxPeronal.NameXXX\AppData\Roaming\Quest Software\Toad Data Point 5.3\Automation Publishing. If you the edit the report it also is saved to similar location. But the path to the tdr IN the automation script is still the old path. So the change you made in tdr during edit mode did not pick up the change.
To get around this I had to "get a copy" of the script. Save to my normal working location. Edit the file and save to normal working location. And then republish and overwrite the script on TIC.
Another note: The path I work out of has to be a public path such as C:\Program Data\Quest Software. If not other Analysts cannot edit or get a copy of the automation script. It this case it errors out because the path cannot be created. Originally I was using a subdirectory of MyDocuements.
That's a lot of work arounds but I'm up and running.