"In other words, can 'instance variables' be defined outside a constructor?"

They can using mop, a module which is planned for inclusion in a future version of Perl (perhaps 5.22 or 5.24), though there's a trial version on CPAN already.

The syntax differs from normal Perl variables, in that instance variables are declared with has instead of my, and instead of having a $ sigil (like $foo) they have a $! twigil (like $!foo).

For example:

use v5.16;
use mop;
use warnings;

class Example {
   has $!name;
   has $!score;
   
   method getName () {
      return $!name;
   }
   
   method getScore () {
      return $!score;
   }
}

my $eg = Example->new(name => "Bob", score => 9.9);

say $eg->getName;
say $eg->getScore;
[download]

The mop module is inspired by the already-existing, and more stable Moose framework. Here's how you'd accomplish the same thing in Moose:

use v5.14;
use warnings;

package Example {
   use Moose;
   has name  => (is => 'ro', reader => 'getName');
   has score => (is => 'ro', reader => 'getScore');
}

my $eg = Example->new(name => "Bob", score => 9.9);

say $eg->getName;
say $eg->getScore;
[download]

Or you could use Moo:

use v5.14;
use warnings;

package Example {
   use Moo;
   has name  => (is => 'ro', reader => 'getName');
   has score => (is => 'ro', reader => 'getScore');
}

my $eg = Example->new(name => "Bob", score => 9.9);

say $eg->getName;
say $eg->getScore;
[download]

Or Moops:

use Moops;

class Example :ro {
   has name  => (reader => 'getName');
   has score => (reader => 'getScore');
}

my $eg = Example->new(name => "Bob", score => 9.9);

say $eg->getName;
say $eg->getScore;
[download]