Inheritance does not work when you access WatchLog and SendEmail as subroutines. In fact for the sake of symmetry I would use a method invokation for AddLocalTime or at least change the name to _AddLocalTime to indicate that it is a local class method intended for use within the class.

use base A ....

sub Schedule {
        my ($self) = @_;

        $self->addTab(_AddLocalTime);
        $self->addTab($self->WatchLog);
        $self->addTab($self->SendEmail); 
}

sub _AddLocalTime {
}
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