I'm not sure that Baumer had the right stuff to succeed doing fine arts painting, and perhaps he came to a similar conclusion. At any rate as early as 1893 his illustrations began appearing in the Pall Mall Gazette, and by 1897 was in Punch, England's leading humor periodical. Besides magazine work, he also illustrated many books -- a list is in the first link, above. By the 1920s, he was doing some portrait painting on the side.
A cartoon from before the era of the strong punchline.
Baumer was also an etcher of some skill.
This is the largest image I could find.
I like this portrait a lot, though can't quite explain why.