Hello Brian, I think your John (Johann)Kaune could be a brother to my Christopher Heinrich Kaune, b abt 1850 in Bremerhaven. I have no further information about him as yet, those Kaune's seem very illusive, but today I found some more previously unknown Kaunes (not mine as yet).
There is or was a sportsclub, called DJK Wesermünde, founded 1928 in Bremerhaven. Founding members were Edmund Kaune (2, senior and junior), Fritz (Friedrich)and Hans Kaune. Also, when Napoleon came through the region, he requested men for his advance on Russia and there was a soldier called Johann Conrad Kaune, a hussar who was taken prisoner in 1812 in Russia. Don't know as yet how and where he fits either. Do you have any further info about anything in Bremerhaven relating to Kaunes?