If one has to spend significant time trying to undertstand the test snippet, how can one really know what is really being tested. What follows are tests which are much more straightforward:

{
   open(local *FILE, '>', 'delete_me.txt') or die;
   print FILE "Test file line $_\n"
      for 1..4;
}

{
   print("Two Handles\n\n");

   open(local *FILE1, '<', 'delete_me.txt') or die;
   open(local *FILE2, '<', 'delete_me.txt') or die;
   print scalar <FILE1>;
   print scalar <FILE1>;
   print scalar <FILE1>;
   print("$.\n");                       # 3 (Line num for FILE1)
   print scalar <FILE2>;
   print("$.\n");                       # 1 (Line num for FILE2)
   print scalar <FILE2>;
   print("$.\n");                       # 2 (Line num for FILE2)
   print scalar <FILE1>;
   print("$.\n");                       # 4 (Line num for FILE1)
}

print("--\n");

{
   print("Does 'seek' Count As an Access?\n\n");

   open(local *FILE1, '<', 'delete_me.txt') or die;
   open(local *FILE2, '<', 'delete_me.txt') or die;
   print scalar <FILE1>;
   print scalar <FILE1>;
   print scalar <FILE1>;
   print("$.\n");                       # 3 (Line num for FILE1)
   seek(FILE2, 0, 0) or die;            # seek counts as an access.
   print("$.\n");                       # 0 (Line num for FILE2)
   print scalar <FILE1>;
   print("$.\n");                       # 4 (Line num for FILE1)
}

print("--\n");

{
   print("Does 'eof' Count As an Access?\n\n");

   open(local *FILE1, '<', 'delete_me.txt') or die;
   open(local *FILE2, '<', 'delete_me.txt') or die;
   print scalar <FILE1>;
   print scalar <FILE1>;
   print scalar <FILE1>;
   print("$.\n");                       # 3 (Line num for FILE1)
   eof(FILE2);                          # eof counts as an access.
   print("$.\n");                       # 0 (Line num for FILE1)
   print scalar <FILE1>;
   print("$.\n");                       # 4 (Line num for FILE1)
}

print("--\n");

{
   print("Does 'read' Count As an Access?\n\n");

   open(local *FILE1, '<', 'delete_me.txt') or die;
   open(local *FILE2, '<', 'delete_me.txt') or die;
   print scalar <FILE1>;
   print scalar <FILE1>;
   print scalar <FILE1>;
   print("$.\n");                       # 3 (Line num for FILE1)
   read(FILE2, my $buf='', 1) or die;   # read doesn't count
   print("$.\n");                       # 3 (Line num for FILE1)
   print scalar <FILE1>;
   print("$.\n");                       # 4 (Line num for FILE1)
}

print("--\n");

{
   print("Assigning to \$.\n\n");

   open(local *FILE, '<', 'delete_me.txt') or die;
   print scalar <FILE>;
   print scalar <FILE>;
   print scalar <FILE>;
   print("$.\n");                       # 3
   $. = 7;                              # Works like "#line"
   print("$.\n");                       # 7
   print scalar <FILE>;                 # Prints the 4th line.
   print("$.\n");                       # 8
}

unlink 'delete_me.txt';
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