I was facing same problem. Emails were not delivering via Gmail SMTP, I have tested everything CSF was fine, I was able to send emails through SMTP via a WordPress plugin to my WordPress blog hosted on same server but not through WHMCS.
I tried everything by disabling CSF, by removing cPanel's smtp restrictions and whatever I can do but it was not working for me. However I just re-write the password again although it was saved already but after doing this it has started working.