Paul is found on http://www.ellisisland.org/ entering Ellis Island on 6 separate occasions. It's a free search site.

If possible, you should get a 2 week free trial to Ancestry because Paul did alot of traveling and he's on several passenger lists and he also applied for a passport which includes a photo of him.

1920 Warren Census::
Paul C. Gonzenbach age 48, widow, he and his parents born in Switzerland. He's an importer for the railroad and immigrated in 1890.
Walter age 21, son, born in NY
Albert C. age 18,son, born in Ecuador
Louisita age 15,dau, born in Ecuador
Louisa age 71, mother-in-law, born in Switzerland

Here's a few misc records I found::

1897 Brooklyn City Directory:
Albert Gonzenbach-bookkeeper, house 345 Liberty Ave
Paul Gonzenbach-bookkeeper, house 346 Liberty Ave
Charles Gonzenbach, embroiderer, house 160 Miller Ave.

Found this in New York Times and it could be Albert (Paul's brother?):
A.C. Gonzenbach, 346 Liberty Ave Brooklyn, died Feb 23, 1901, age 25

Ernest Von Gonzenbach, naturalized at the Kings County New York Court House, Feb 6, 1893. Witness :Charles Albert Von Gonzenbach.

Paul Gonzenbach married Louise in Kings County on Jan 29, 1898.

Warren, RI City Directory::
1906 Charles A. Gonzenbach, house on Railroad Ave. Wiiliam Gonzenbach also of same address

1913 Paul Gonzenbach, importer, bds Cole St
Charles A. Gonzenbach (CA Gonzenbach & Co.), 4 Cole St
CA Gonzenbach, Treasurer of Swiss Textile Co.

Found this on a passenger list and wondered if he was a relation of Paul::

Friederick Von Gonzenbach, born abt 1872 in Hampswerl, Switzerland. He arrived in NY in 1909 and was a merchant.