diff --git a/.github/workflows/cpp_extra.yml b/.github/workflows/cpp_extra.yml
index 5aaad7f39332..a3dcc2b21fc1 100644
--- a/.github/workflows/cpp_extra.yml
+++ b/.github/workflows/cpp_extra.yml
@@ -414,7 +414,7 @@ jobs:
       needs.check-labels.outputs.force == 'true' ||
       contains(fromJSON(needs.check-labels.outputs.ci-extra-labels || '[]'), 'CI: Extra') ||
       contains(fromJSON(needs.check-labels.outputs.ci-extra-labels || '[]'), 'CI: Extra: C++')
-    timeout-minutes: 75
+    timeout-minutes: 120
     strategy:
       fail-fast: false
       matrix:
diff --git a/cpp/src/arrow/flight/sql/odbc/tests/CMakeLists.txt b/cpp/src/arrow/flight/sql/odbc/tests/CMakeLists.txt
index e0e562f2d255..0f45bfd0c811 100644
--- a/cpp/src/arrow/flight/sql/odbc/tests/CMakeLists.txt
+++ b/cpp/src/arrow/flight/sql/odbc/tests/CMakeLists.txt
@@ -42,12 +42,14 @@ set(ARROW_FLIGHT_SQL_ODBC_TEST_SRCS
     # GH-46889: move protobuf_test_util to a more common location
     ../../../../engine/substrait/protobuf_test_util.cc)
 
-if(ARROW_TEST_LINKAGE STREQUAL "static")
-  set(ARROW_FLIGHT_SQL_ODBC_TEST_LINK_LIBS arrow_flight_sql_odbc_static
-                                           ${ARROW_TEST_STATIC_LINK_LIBS})
-else()
+# GH-49651 Link ODBC tests statically on Linux and dynamically on macOS/Windows
+if(WIN32 OR APPLE)
   set(ARROW_FLIGHT_SQL_ODBC_TEST_LINK_LIBS arrow_flight_sql_odbc_shared
                                            ${ARROW_TEST_SHARED_LINK_LIBS})
+else()
+  # GH-49651 Link ODBC tests statically on Linux to fix segfault
+  set(ARROW_FLIGHT_SQL_ODBC_TEST_LINK_LIBS arrow_flight_sql_odbc_static
+                                           ${ARROW_TEST_STATIC_LINK_LIBS})
 endif()
 
 # On macOS, link `ODBCINST` first to ensure iodbc take precedence over unixodbc
@@ -65,6 +67,13 @@ else()
   # Unix
   list(APPEND ARROW_FLIGHT_SQL_ODBC_TEST_STATIC_LINK_LIBS
        ${ARROW_FLIGHT_SQL_ODBC_TEST_LIBS} ${ARROW_FLIGHT_SQL_ODBC_TEST_LINK_LIBS})
+
+  if(NOT APPLE)
+    # Links static dependencies on Linux to support ARROW_TEST_LINKAGE=static
+    list(APPEND ARROW_FLIGHT_SQL_ODBC_TEST_STATIC_LINK_LIBS arrow_odbc_spi_impl
+         ${ARROW_PROTOBUF_LIBPROTOBUF})
+  endif()
+
 endif()
 
 add_arrow_test(flight_sql_odbc_test