maybe a little example will make it clearer

  DB<1> sub tst  {return undef}
  
  DB<2> if ($a=tst()) {print "TRUE"} else {print "FALSE" }
FALSE
  DB<3> if (@a=tst()) {print "TRUE"} else {print "FALSE" }
TRUE
  DB<4> sub tst  { return (); }
  
  DB<5> if ($a=tst()) {print "TRUE"} else {print "FALSE" }
FALSE
  DB<6> if (@a=tst()) {print "TRUE"} else {print "FALSE" }
FALSE
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line 4 is of course redundant, return; and  return (); do exactly the same thing.

> I have found it wise to always return an explicit value,

OK, if you wanna code more "explicitly", you should better define constants for TRUE, FALSE and FAILED.

  DB<9> use constant FAILED => ();
 
  DB<10> use constant FALSE => !1;
 
  DB<11> use constant TRUE => 1;
 
  DB<12> sub t_FALSE  { return FALSE; }
 
  DB<13> sub t_TRUE  { return TRUE; }
 
  DB<14> sub t_FAILED  { return FAILED; }
 
  DB<15> if (@a=t_FAILED) {print "TRUE"} else {print "FALSE" }
FALSE
  DB<16> if (@a=t_FALSE) {print "TRUE"} else {print "FALSE" }
TRUE
  DB<17> if ($a=t_FALSE) {print "TRUE"} else {print "FALSE" }
FALSE
  DB<18> if ($a=t_FAILED) {print "TRUE"} else {print "FALSE" }
FALSE
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If you wonder about my definition of FALSE, see Truth and Falsehood in perlsyn:

       Negation of a true value by "!" or "not" returns a special fals
+e value.
       When evaluated as a string it is treated as '', but as a number
+, it is
       treated as 0.
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UPDATE:

please note: FALSE is defined!

  DB<27> p !defined (FAILED)
1
  DB<28> p defined (FALSE)
1
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i.e. FALSE acts like a defined value like in most other languages.

UPDATE:

On second thought FAILED should better be named EMPTY or NOTHING. Failure is just an interpretation of returning nothing.