diff --git a/dev/tasks/homebrew-formulae/apache-arrow.rb b/dev/tasks/homebrew-formulae/apache-arrow.rb
index 9086fdaae4ab4..f5d7ff36ea041 100644
--- a/dev/tasks/homebrew-formulae/apache-arrow.rb
+++ b/dev/tasks/homebrew-formulae/apache-arrow.rb
@@ -57,7 +57,8 @@ class ApacheArrow < Formula
   fails_with gcc: "5"
 
   def install
-    # https://github.com/Homebrew/homebrew-core/issues/76537
+    # This isn't for https://github.com/Homebrew/homebrew-core/issues/76537 .
+    # This may improve performance.
     ENV.runtime_cpu_detection if Hardware::CPU.intel?
 
     # link against system libc++ instead of llvm provided libc++
@@ -90,6 +91,11 @@ def install
       -DARROW_WITH_ZSTD=ON
       -DPARQUET_BUILD_EXECUTABLES=ON
     ]
+    # Disable runtime SIMD dispatch. It may cause "illegal opcode"
+    # error on Intel Mac because of one-definition-rule violation.
+    #
+    # https://github.com/apache/arrow/issues/36685
+    args << "-DARROW_RUNTIME_SIMD_LEVEL=NONE" if OS.mac? and Hardware::CPU.intel?
 
     system "cmake", "-S", "cpp", "-B", "build", *args, *std_cmake_args
     system "cmake", "--build", "build"
diff --git a/dev/tasks/macros.jinja b/dev/tasks/macros.jinja
index 475494af18ce6..1f2f9a72975eb 100644
--- a/dev/tasks/macros.jinja
+++ b/dev/tasks/macros.jinja
@@ -214,6 +214,7 @@ on:
       # see https://github.com/actions/runner-images/issues/6868
       brew install --overwrite python@3.11 python@3.10
 
+      set -x
       ARROW_GLIB_FORMULA=$(echo ${ARROW_FORMULA} | sed -e 's/\.rb/-glib.rb/')
       echo "ARROW_GLIB_FORMULA=${ARROW_GLIB_FORMULA}" >> ${GITHUB_ENV}
       for formula in ${ARROW_FORMULA} ${ARROW_GLIB_FORMULA}; do
@@ -223,11 +224,12 @@ on:
         # Pin the current commit in the formula to test so that
         # we're not always pulling from the tip of the default branch
         sed -i '' -E \
-          -e 's@https://github.com/apache/arrow.git"$@{{ arrow.remote }}.git", revision: "{{ arrow.head }}"@' \
+          -e 's@https://github.com/apache/arrow.git", branch: "main"$@{{ arrow.remote }}.git", revision: "{{ arrow.head }}"@' \
           ${formula}
         # Sometimes crossbow gives a remote URL with .git and sometimes not.
         # Make sure there's only one
         sed -i '' -E -e 's@.git.git@.git@' ${formula}
+        cat ${formula}
         cp ${formula} $(brew --repository homebrew/core)/Formula/
       done
 {% endmacro %}
diff --git a/dev/tasks/r/github.macos.brew.yml b/dev/tasks/r/github.macos.brew.yml
index dea7564c5f80f..8a0e6f6bb96e3 100644
--- a/dev/tasks/r/github.macos.brew.yml
+++ b/dev/tasks/r/github.macos.brew.yml
@@ -24,21 +24,33 @@ jobs:
     name: "Homebrew + R package"
     runs-on: macOS-11
     steps:
+      - name: Show system information
+        run: |
+          sysctl hw.optional machdep.cpu
+
       {{ macros.github_checkout_arrow()|indent }}
 
       {{ macros.configure_homebrew_arrow(formula)|indent }}
       - name: Install apache-arrow
         env:
-        {{ macros.github_set_sccache_envvars()|indent(8)}}  
+        {{ macros.github_set_sccache_envvars()|indent(8)}}
         run: |
-          
           brew install sccache
           # for testing
           brew install minio
-          
+
           # TODO(ARROW-16907): apache/arrow@main seems to be installed already
           # so this does nothing on a branch/PR
-          brew install -v --HEAD apache-arrow
+          brew install -v --HEAD {{ '$(brew --repository homebrew/core)/Formula/apache-arrow.rb' }}
+
+          mkdir -p homebrew-logs
+          cp -a ~/Library/Logs/Homebrew/apache-arrow homebrew-logs/
+      - name: Save logs
+        if: always()
+        uses: actions/upload-artifact@v2
+        with:
+          name: homebrew-logs
+          path: homebrew-logs
 
       - uses: r-lib/actions/setup-r@v2
       - name: Install dependencies