diff -up src/sage/all.py.orig src/sage/all.py
--- src/sage/all.py.orig	2020-10-24 11:37:59.000000000 -0600
+++ src/sage/all.py	2020-10-30 13:56:32.674557350 -0600
@@ -324,11 +324,11 @@ def _write_started_file():
     Check that the file exists when Sage is running (note, this file is not
     necessarily installed or used by downstream packages of Sage)::
 
-        sage: started_file = os.path.join(SAGE_LOCAL, 'etc', 'sage-started.txt')
+        sage: started_file = os.path.join(DOT_SAGE, 'sage-started.txt')
         sage: os.path.isfile(started_file)  # optional - build
         True
     """
-    started_file = os.path.join(SAGE_LOCAL, 'etc', 'sage-started.txt')
+    started_file = os.path.join(DOT_SAGE, 'sage-started.txt')
 
     # Current time with a resolution of 1 second
     import datetime