Just noticed something that may explain my previous findings.
From the tz variable man page:

http://www.gnu.org/software/libc/manual/html_node/TZ-Variable.html

"If characters begins with a slash, it is an absolute file name; otherwise the library looks for the file /usr/share/zoneinfo/characters."

Thus starting with a period is what throws it off?

-Matt

From: tz <tz-bounces@iana.org> on behalf of Paul Eggert <eggert@cs.ucla.edu>
Sent: Monday, October 29, 2018 8:47 AM
To: Arthur David Olson
Cc: Time Zone Mailing List
Subject: Re: [tz] zdump bug?
 
On 10/28/18 9:23 PM, Paul Eggert wrote:
> 'zdump New_York' is treated differently from 'zdump ./New_York'. It
> might make sense for the code to try harder to treat only ".."
> components differently.

I installed the attached first patch to try to do that. The second
attached patch silences a warning when running "make
CFLAGS='$(GCC_DEBUG_FLAGS)' GCC_INSTRUMENT=" on my platform (I updated
GCC recently).