diff --git a/yt_dlp/downloader/external.py b/yt_dlp/downloader/external.py
index 82bc5106a5..14879b358d 100644
--- a/yt_dlp/downloader/external.py
+++ b/yt_dlp/downloader/external.py
@@ -457,6 +457,8 @@ class FFmpegFD(ExternalFD):
 
     @classmethod
     def available(cls, path=None):
+        # TODO: Fix path for ffmpeg
+        # Fixme: This may be wrong when --ffmpeg-location is used
         return FFmpegPostProcessor().available
 
     def on_process_started(self, proc, stdin):
diff --git a/yt_dlp/postprocessor/ffmpeg.py b/yt_dlp/postprocessor/ffmpeg.py
index 5c9c0390d9..a850bdd102 100644
--- a/yt_dlp/postprocessor/ffmpeg.py
+++ b/yt_dlp/postprocessor/ffmpeg.py
@@ -192,7 +192,10 @@ class FFmpegPostProcessor(PostProcessor):
 
     @property
     def available(self):
-        return bool(self._ffmpeg_location.get()) or self.basename is not None
+        # If we return that ffmpeg is available, then the basename property *must* be run
+        # (as doing so has side effects), and its value can never be None
+        # See: https://github.com/yt-dlp/yt-dlp/issues/12829
+        return self.basename is not None
 
     @property
     def executable(self):