Get product by ID or category to send email for purchase of a certain product

I am trying to send customers an email if they purchase one of three specific products out of all of my products. The three products have a category of “waiting-list.” The product IDs I want this email to go out for are 6771, 6662, and 6658.

I am using SkyVerge’s custom email template and it is working, except that it sends the email out for all product purchases, not just the three I want it sent for.

The line that I am having trouble with is the one that will return the function if the requirement is not met. I have tried several things:

// bail if product category is not waiting list
	if ( is_product_category('waiting-list') )
        return;

The code above sends the email out for all product purchases, not just for products with the category of ‘waiting-list’

// bail if product category is not waiting list
	if ( ! is_product_category('waiting-list') )
        return;

The code above doesn’t send the email out at all. And for the product I am testing this on, the only product category selected for it is waiting-list.

// bail if product category is not one of these product IDs 6771, 6662, 6658
	$product = get_product( $post->ID );
line 69:	if ( ! in_array( $this->object->$product(), array( '6771', '6662', '6658' ) ) )
        return;

The code above was another try. I was hoping to have the email sent out for exact products, instead of a product category. It returns an error. Fatal error: Method name must be a string in /home/content/50/10079350/html/PFmeats/wp-content/plugins/woocommerce-waitinglist-email/includes/class-wc-waitinglist-email.php on line 69

My site is https://www.pasturefreshmeats.com (using WooCommerce 2.1.12) and the product to test is CSA Membership: Green Beef Waiting List.

I’m fairly new to PHP but I understand how to read and edit the code, I’m just not very good at writing it yet! Thanks for any help you can provide.