Nice to see you are understanding how to use the pluggin
I mean sending UHTMLMails from an new file (customers.php) and you create a new module for this useing the pattern supposed to be used.
Well can't honestly see no problems with your tep_mail function.
The tep_mail code will clearly be parsed as you say that the code for outputting the dubug prewiev is reached... and you get no error message...
You have set "Configuration" --> "E-Mail Options" --> "Send E-Mails" = false
This should be set to true.
Is that the solution?
'Send E-Mails' is set to 'True' (I never turned it off lol)
I just dont see why it is not sending the emails because as you say it is creating the html email and saving it in debug format.