Borrow parts of the description of ^^ from the synopsis to describe how it really behaves when all the arguments are false.

Author: pmurias

doc/Language/operators.pod6

@@ -1723,11 +1723,16 @@ true value, the arguments to the right of are never evaluated.
 
 =head2 infix C«^^»
 
-Returns the first true argument if there is only one, and L<Nil> otherwise.
-Short-circuits as soon as two true arguments are found.
+X<Short-circuit exclusive-or>. Returns the true argument if there
+is one (and only one).  Returns the last argument if all arguments are false.
+Returns C<Nil> otherwise (when more than one argument is true).
+
+This operator short-circuits in the sense that it does not evaluate
+any arguments after a 2nd true result.
 
     say 0 ^^ 42;                # 42
-    say 0 ^^ 42 ^^ 1 ^^ die 8;  # (empty line)
+    say '' ^^ 0;                # 0
+    say 0 ^^ 42 ^^ 1 ^^ die "never called";  # (empty line)
 
 Note that the semantics of this operator may not be what you assume: infix C«^^»
 flips to first true value it finds, and then flips to Nil I<forever> after the