The mysterious monk's advice is incomplete. Trying this approach from the command line shows the problem:

#!perl

for $invalue (qw/ 1 -10 abc /) {

    eval{ local $^W = 1; $invalue + 0 };   ### Is Number?
    if ( $@ ) {
        print "$invalue is *not* a Number; Details: $@\n";
    } else {
        print = "$invalue appears to be a number.\n";
    }

}
[download]

produces:

1 appears to be a number.
-10 appears to be a number.
Argument "abc" isn't numeric in add at num.pl line 3.
abc appears to be a number.
[download]

The reason for this is that eval only traps errors, not warnings. The warning is printed directly to STDERR and $@ remains empty.

To fix this, you need to force the warning into an error. (And add an empty list assignment to silence the void context warning.):

#!perl

for $invalue (qw/ 1 -10 abc /) {

    eval{ local $SIG{__WARN__} = sub { die @_ };
          local $^W = 1; () = $invalue + 0 };   ### Is Number?
    if ( $@ ) {
        print "$invalue is *not* a Number; Details: $@\n";
    } else {
        print "$invalue appears to be a number.\n";
    }

}
[download]

produces:

1 appears to be a number.
-10 appears to be a number.
abc is *not* a Number; Details: Argument "abc" isn't numeric in add at
+ num.pl line 4.
[download]