I'm pretty sure I saw the caricature artist in Downtown Disney a couple weeks ago. I don't remember seeing it in either park. The silhouette artist at DL was very busy though.
I don't remember the exact area in Downtown Disney, but this seems correct.
There is definitely one outside Blue Bayou in Disneyland, like you said. And there is also one in DCA outside Knick's Knacks at the top of Pixar Pier (across from Lamplight Lounge).