I think I have figured out the what, it’s just the who, when, where and why that I don’t have the answer to.
In 1995 during Phase I of the X-33 program NASA received proposals from Rockwell, McDonnell Douglas, and Lockheed Martin. In 1996 NASA selected Lockheed Martin's proposal.
In the artist's rendition of the McDonnell Douglas proposal a cartoon character can be seen on the tail of the spaceship.
Artist's rendition of McDonnell Douglas X-33 Proposal (Source: NASA, www.dfrc.nasa.gov)
The artist even put a discernible reflection of the character on the fuselage next to the character.
The character appears to be what is known as the McDonnell Douglas F-4 Phantom II "Spook", as seen in the photo of a Phantom II patch in Wikimedia Commons, the photo of the Spook patch can also be seen on the Wikipedia page for the F-4 Phantom.
According to Boeing’s website: secure.boeingimages.com
McDonnell Aircraft technical presentations artist Anthony "Tony" Wong created the Phantom II "spook" character, first used on a shoulder patch for F-4 crew members in 1958. It quickly became the unofficial mascot for many members of the F-4 Phantom community across the globe.
Some additional information about the Phantom II Spook character is found in Wikipedia: en.wikipedia.org
The name "Spook" was coined by the crews of either the 12th Tactical Fighter Wing or the 4453rd Combat Crew Training Wing at MacDill AFB. The figure is ubiquitous, appearing on many items associated with the F-4.
Since the F-4 Phantom was built by McDonnell Douglas there would be that connection. But there must have been some other reason for the placement of the Spook cartoon in the X-33 drawing.
The artist's rendition was created by J. Frassanito & Associates www.frassanito.com, a design company located near the Johnson Space Center in Houston which has done a lot of computer graphics work for NASA over the years. However it seems unlikely that anyone working at that company decided to put a cartoon on the drawing. It would have had to have been requested by someone at McDonnell Douglas who was involved with the project, and presumably approved by the managers of the project.
It could be that one or more of the engineers and managers on the X-33 proposal project were former F-4 pilots. In fact one of them was for sure, Pete Conrad.
Apollo 12 crew Pete Conrad, Richard Gordon, Alan Bean (Source: NASA, via Wikimedia Commons)
Pete Conrad was a former astronaut in both Gemini and Apollo, and in fact commanded the second Moon landing Apollo 12. Among other things he is famous for his quip after stepping down onto the Lunar Module footpad when he said, “that may have been a small one for Neil, but that's a long one for me.”
In fact it’s worth taking a moment to read the full Conrad quote as well as the commentary from a 1990’s interview that Eric Jones, who created the Apollo Lunar Surface Journal, had with Conrad and Lunar Module pilot Alan Bean, in order to get a glimpse of Conrad's humor which was legendary.
Conrad: "Whoopie! Man, that may have been a small one for Neil, but that's a long one for me."
[Jones - "I understand that there was a bet on your saying that."]
[Bean - "Who'd you bet?"]
[Conrad - "You know who I bet."]
[Bean - "Nope. I forget."]
[Conrad - "A reporter, who thought the government put words in our mouths."]
[Bean - "Oh!"]
[Conrad - (Laughing) "I also had $500 riding on it, but I never got paid."]
Apollo Lunar Surface Journal timestamp 115:22:16
After leaving NASA Conrad went to work for McDonnell Douglas as a vice president and consultant. He became heavily involved in the DC-X project, and in fact Conrad was involved in remotely piloting the DC-X during flight tests space.nss.org
Test flights of the DC-X were ongoing in 1995 when McDonnell Douglas submitted their proposal for the X-33. It is not known to what extent their X-33 proposal mirrored the DC-X, but it can probably be assumed that the two designs were similar.
Prior to joining NASA as an astronaut Pete Conrad flew a McDonnell Douglas F-4 Phantom II for the Navy.
I suspect that the Pete Conrad connection is as close as we can get with theory, unless someone is able to find some definitive evidence for why the cartoon was in the artist's rendition.