There's an interesting distinction between grandiose and vulnerable narcissists.
The latter subset have a statistically significant increase in how often they refer to themselves in writing.
A while back I decided to measure that variable in the Biblical Epistles given language that struck me as rather indicative of vulnerable narcissism through the Pauline Epistles.
Indeed, the relative amount of personal reference in Paul's undisputed letters (except Thessalonians which is from 3 people) is at around 20-40% whereas for undisputed non-Pauline letters it's around 2-10%.
Applying this metric to the disputed letters, only one falls in the range of the undisputed (2 Timothy).
I plan on rolling this into some further analysis down the road, but it's a fun little historical detail I think of every time I see vulnerable narcissism discussed.