currently, no template is there for partial payment. You have to follow the below steps to implement :You have to create an email template in the hotelcommerce/mails/ folder for the partial payment. (put the email template in all language folders) Then you have to attach that email Template with the status by checking "Send an email to the customer when his/her order status has changed". Now you have to append data for the partial payment email. Mails are sent from function sendEmail() (line number : 410) in the class hotelcommerce/classes/order/OrderHistory.php. So you have to set the data (Data will be depended on what is needed in the partial payment email template created by you) here. If you do the above steps correctly you will be able to send email successfully.
Hope you understand the process.
Thanks & Regards.