Zoho Books Connector - Update Customer

I think there's a problem with the Zoho Books Update Customer connector in Flow.

I have a Flow to add or update Books customers who buy on our WooCommerce site. The logic is that the email is passed from WooCommerce and a Books Fetch Customer operation is initiated. If the response is not null, then a Books Update Customer operation is intiated.

The problem is with the email field in the Update Customer module.

If I leave it blank, the customer is updated with no email address.

If I fill in the email address (which, because of previous logic, will always be the same as what is already on record), Zoho Flow errors out on the Update Customer step, with the message "Zoho Books says "The email address you're about to add/update already exists within the contact (Contact or associated contact persons). Make sure that the email address you provide is unique."

How does one update the customer while not changing their email address?