The problem is that you're calling exists on a subroutine reference for actions 1 and 2. Why not test for something else, such as a HASH reference or a CODE reference using ref? What about:

sub get_config_item {
    my( $runmodes, $action ) = @_;
    my $config_item = $runmodes->{ config_item };

    if( ref $runmodes->{ $action } eq 'HASH' ) { # error line
        &{ $runmodes->{ $action }{ subroutine }};
        $config_item = $runmodes->{ $action }{ config_item };
    }
    else {
        &{ $runmodes->{ $action }}
    }

    return $config_item;
}
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Honestly though, this looks to me like a candidate for refactoring, as the contortions that you're now enduring will only get worse as the code expands over time.

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"The dead do not recognize context" -- Kai, Lexx