GH-48932: [C++][Packaging][FlightRPC] Fix rsync build error ODBC Nightly Package

.github/workflows/cpp_extra.yml

@@ -457,16 +457,32 @@ jobs:
           name: flight-sql-odbc-msi-installer
           path: build/cpp/Apache Arrow Flight SQL ODBC-*-win64.msi
           if-no-files-found: error
-      # Upload ODBC installer as nightly release in scheduled runs
+
+  odbc-nightly:
+    needs: odbc
+    name: ODBC nightly
+    runs-on: ubuntu-latest
+    if: github.event_name == 'schedule' && github.repository == 'apache/arrow'
+    steps:
+      - name: Download the artifacts
+        uses: actions/download-artifact@v7
+        with:
+          name: flight-sql-odbc-msi-installer
       - name: Prepare ODBC installer for sync
-        if: github.event_name == 'schedule'
         run: |
           mkdir odbc-installer
-          Move-Item "build/cpp/Apache Arrow Flight SQL ODBC-*-win64.msi" odbc-installer/
-          tree odbc-installer /f
+          mv *.msi odbc-installer/
+          tree odbc-installer
+      - name: Checkout Arrow
+        uses: actions/checkout@v6
+        with:
+          fetch-depth: 1
+          path: arrow
+          repository: apache/arrow
+          ref: main
+          submodules: recursive
       - name: Sync to Remote
-        if: github.event_name == 'schedule'
-        uses: ./.github/actions/sync-nightlies
+        uses: ./arrow/.github/actions/sync-nightlies
         with:
           upload: true
           switches: -avzh --update --delete --progress