It's a little bit more complicated than it seems from first glancing at the 'asia' file, because of the inclusion of the 'RussiaAsia' and 'EUAsia' rulesets.
`zdump` makes this somewhat clearer, though running the outputs through `diff` alone is only minimally helpful as all the transitions since 1992-09-27 are at least slightly different. So, to help make clearer comparisons between proximal transitions, I sorted the outputs by date:
diff -U0 <(./zdump -i Asia/Baku) <(./zdump -i Asia/Yerevan) | sort -k 1.2
+++ /dev/fd/62 2019-07-21 12:43:51.000000000 -0400
+- - +0258 LMT
-- - +031924 LMT
--- /dev/fd/63 2019-07-21 12:43:51.000000000 -0400
-1924-05-01 23:40:36 +03
+1924-05-02 00:02 +03
+1992-09-27 02 +03
-1992-09-27 03 +04
+1993-03-28 03 +04 1
+1993-09-26 02 +03
+1994-03-27 03 +04 1
+1994-09-25 02 +03
+1995-03-26 03 +04 1
+1995-09-24 03 +04
-1996-03-31 06 +05 1
-1996-10-27 05 +04
+1997-03-30 03 +05 1
-1997-03-30 05 +05 1
+1997-10-26 02 +04
-1997-10-26 04 +04
+1998-03-29 03 +05 1
-1998-03-29 05 +05 1
+1998-10-25 02 +04
-1998-10-25 04 +04
+1999-03-28 03 +05 1
-1999-03-28 05 +05 1
+1999-10-31 02 +04
-1999-10-31 04 +04
+2000-03-26 03 +05 1
-2000-03-26 05 +05 1
+2000-10-29 02 +04
-2000-10-29 04 +04
+2001-03-25 03 +05 1
-2001-03-25 05 +05 1
+2001-10-28 02 +04
-2001-10-28 04 +04
+2002-03-31 03 +05 1
-2002-03-31 05 +05 1
+2002-10-27 02 +04
-2002-10-27 04 +04
+2003-03-30 03 +05 1
-2003-03-30 05 +05 1
+2003-10-26 02 +04
-2003-10-26 04 +04
+2004-03-28 03 +05 1
-2004-03-28 05 +05 1
+2004-10-31 02 +04
-2004-10-31 04 +04
+2005-03-27 03 +05 1
-2005-03-27 05 +05 1
+2005-10-30 02 +04
-2005-10-30 04 +04
+2006-03-26 03 +05 1
-2006-03-26 05 +05 1
+2006-10-29 02 +04
-2006-10-29 04 +04
+2007-03-25 03 +05 1
-2007-03-25 05 +05 1
+2007-10-28 02 +04
-2007-10-28 04 +04
+2008-03-30 03 +05 1
-2008-03-30 05 +05 1
+2008-10-26 02 +04
-2008-10-26 04 +04
+2009-03-29 03 +05 1
-2009-03-29 05 +05 1
+2009-10-25 02 +04
-2009-10-25 04 +04
+2010-03-28 03 +05 1
-2010-03-28 05 +05 1
+2010-10-31 02 +04
-2010-10-31 04 +04
+2011-03-27 03 +05 1
-2011-03-27 05 +05 1
+2011-10-30 02 +04
-2011-10-30 04 +04
-2012-03-25 05 +05 1
-2012-10-28 04 +04
-2013-03-31 05 +05 1
-2013-10-27 04 +04
-2014-03-30 05 +05 1
-2014-10-26 04 +04
-2015-03-29 05 +05 1
-2015-10-25 04 +04
@@ -2,3 +2,3 @@
@@ -29,41 +29,37 @@
-TZ="Asia/Baku"
+TZ="Asia/Yerevan"
As the last lines in the output above make reasonably clear, a '-' line indicates a line appearing only in the output for Asia/Baku (Azerbaijan) and '+' lines are for Asia/Yerevan (Armenia).
To me, there are five distinct periods that stand out:
(1) On 1992-09-27, Azerbaijan moved permanently forward to +04, while Armenia retained its ongoing seasonal shift from +03 to +04 through 1995-09-24.
(2) In 1996, the situation was somewhat flipped, with Armenia staying permanently on +04 while Azerbaijan employed a further seasonal shift to +05.
(3) Between 1997-03-30 and 2011-10-30, both used +04/+05, and transitioned to and from DST on the same dates, though at slightly different times — typically two hours apart, as Armenia would change at 02:00s (that is, 02:00 +04, or 22:00Z) while Azerbaijan would change at 04:00 +04 or 05:00 +05 (equivalently, 04:00s, or 00:00Z). Given the ever-so-slight differences here, it would take some careful reference-checking to determine what exactly Nagorno-Karabakh did during this period. However, with 30 transitions, it's certainly possible such sources could be found.
(4) From 2012 through 2015, only Azerbaijan continued to observe DST. It could be interesting to determine whether the "enclave" went along with their Azerbaijani surroundings, or whether it followed Armenia and stayed on +04.
(5) From 2016 to present, both countries just observe year-round +04. Nothing interesting there.
Of these, (1), (2), and (4) are of the greatest potential interest. In particular, bits of (1) may be harder to verify since it is close to the fall of the Soviet Union. (2) and (4) are at least similar situations. (3) likely just boils down to minor technicalities which may wade further into the past and present politics of the region than is warranted, unless there happen to exist any clear authoritative sources which can be easily found.