Sebastian is a minor character who enters in Act II, scene i. Since he plays a minor--though important--role, it takes more work to analyze his character. We first learn that he is depressed yet considerately forbids Antonio from accompanying as he thinks he might bring bad luck to his rescuer:
My stars shine darkly over
me: the malignancy of my fate might perhaps
This also shows that he is courageous because only a courageous person will venture on a darkened path of sorrow without companionship. When compared to Viola, Sebastian differs from her in that while she was sorrowful and frightened of her future ("O that I served that lady / And might not be delivered to the world,"), he is depressed by circumstances. Yet they are the same in that they both are courageous in their quest to meet their fate. His courage is confirmed in IV. i when he fights with Sirs Andrew and Toby. Sebastian also loved Viola dearly:
She is drowned already, sir, with salt water, though I seem to drown her remembrance again with more.
Another trait that is revealed about Sebastian is that he does not succumb to his depression for long: he replaces it with healthful activity when in III. iii he decides to sight-see:
let us satisfy our eyes
With the memorials and the things of fame
That do renown this city.
Another trait is that Sebastian is willing to acceptance deliverance from his loss through the seemingly mad behavior of Olivia--she is a beautiful countess, so what is there to complain of: "If it be thus to dream, still let me sleep!"