From the municipal register of population (book 120 folio 156):
Tapphorn, Theodor Godfried born 1838 in Cloppenburg, Roman Catholic, arrived
in Rotterdam on 29th september 1854 , last lived Cloppenburg, occupation:
There is a note attached: left 30th januari 1856.

We couldn't find out where he was going when he left in 1856.

Could a connection with the American Civil War be true?

I'm not aware of any electronic shipping register that lists the passengers
from Rotterdam.