Emails not sending

Certain emails are being sent and certain emails are not being sent. I can’t isolate what allows certain ones to be sent and the others to not be sent. All emails are enabled. If the plugin (Email template customizer) is disabled, all emails send fine so the problem is with the plugin itself or compatibility with another plugin. I have tried disabling many other plugins but no difference.

ORDER ON HOLD:

If a customer pays with BACS, the admin email is sent (to myself) but the customer receives NO email.

If a customer pays with cash on delivery, an order on hold email should be sent also – but no email is sent (no admin, no customer)

I have no idea what has been causing this and have been trying to find the root for weeks. Can you please assist?