PUZZLED

You are 13 down
And always 2 across
You are never 1 down
And sadly not 19 across
You are six letters
Starting with a T
You are coffee time
And an acrostic too
As well as cryptic
Lets try 11 down
Followed by three across
Which is what the canines do
You to be 7 down
I have never known
A dictionary won’t help me
Nor a thesaurus
For like most women
You are an unsolved puzzle