Yes, you can look for a naturalization record often these don't provide specific towns of origins however they do typically note the country of origin or to whom they were renouncing their previous citizenship.
Eileen has done a wonderful job locating them in Canton, IL!
Bravo!! It still begs the question why did he and his brother/cousin part ways?
The following website is a great place to start your Elger research in New Berlin: http://www.linkstothepast.com/waukesha/index.php
From the notes there, it appears the Elgers were members of the old German Reformed church. Since you have a specific date for Francis Elger's death - you could have them look for an obit and the church burial record based upon the church noted in the obit.
Regardless of why they parted ways - they clearly came together to the US. And that family has clearly indicated Bohemia in their census records. So, the German - Austria - Bohemia theme certainly matches.
Best of luck in your research. If it was me, I would go for Francis's obit (German and English newspapers in New Berlin or Milwaukee) - Gary Rebholz has done an unbelieveable job in indexing families that appeared in the German newspapers in Milwaukee - You might reach out to him as I think he does a free search of his index and then you pay for a copy of the extracted info. He has an ancestry account with contact info: firstname.lastname@example.org
Best of luck,