I have lost 6h today trying to figure this out, including installing a local mail server in case there was something wrong with gmail. Turns out there is a glitch in the mail settings form that ignores or overwrites the password when testing email.

Steps to reproduce

Follow exactly:

1. Go to Administration, mail server
2. Type in:
   1. Hostname: smtp.gmail.com
   2. Port: 587
   3. Username: testuser@gmail.com
   4. Password: my_password
   5. [X] Use TLS
   6. Email from: testuser@gmail.com
3. Click [Save]

at this point, the page refreshes. You notice that the number of * in the password field is shorter than your password, but nevertheless continue as follows:

type a recipient: friend@gmail.com
click [Test]

Test email fails due to authentication failure.

WORKAROUND

1. start over.
2. Go to Administration, mail server
3. Type in:
   1. Hostname: smtp.gmail.com
   2. Port: 587
   3. Username: testuser@gmail.com
   4. Password: my_password
   5. [X] Use TLS
   6. Email from testuser@gmail.com

click [Save]

at this point, the page refreshes. You notice that the number of * in the password field is shorter than your password, but continue as follows:

Type again the password:
Password: my_password
type a recipient: friend@gmail.com
click [Test]

test email succeeds.