How we cite our quotes:
(Orestes): "Has some new disaster befallen this house, or would I be right in guessing that these women bring libations for my father, appeasements of the dead? It could never be anything else! Why, I think my sister Electra is there too, conspicuous in bitter grief. O Zeus! Grant me vengeance for my father's death! Be my ally if you will!" (12-19)
Here we see Orestes run through an interesting train of thought. He begins by wondering who the women are who are coming forward with libations. Then, he realizes that they are bringing libations to the tomb of Agamemnon, his father. Once he realizes this, he has an insight into the identity of Electra, his sister. Orestes cannot have seen his sister in living memory. How does he know it's her? Does he recognize a family resemblance with himself? Or is he able to guess based on her behavior; that is to say, does he guess that, because she is "conspicuous in bitter grief," she must be the child of the dead man?
Without ruling out the Option 1 (family resemblance), it's worth thinking about Option 2 (behavior) in connection with some of the other themes of the play. Why would Aeschylus want to introduce the idea that the identity of family members can be guessed from their behavior? Throughout the play, do characters tend to act in accordance with the roles prescribed by their family relations, or do they contradict those roles? Or can different family obligations actually come into conflict?
(Electra): "How am I to speak sensibly to my father, how am I to pray to him? Am I to say that I bring [these mourning-libations] to a dear husband from a dear wife, from my mother? I have no words for that, no words I should say as I pour this offering on my father's tomb." (88-90)
These lines continue a theme that was introduced in the previous quotation: that sometimes, family relations and behavior can come into conflict. Here, Electra doesn't feel that she can make offerings on behalf of her mother Clytemnestra, Agamemnon's former wife, because Clytemnestra did not act like a wife towards him (duh, she killed him).
(Electra): "As I pour these libations to the dead, my own words too call upon my father: have pity on me, and kindle our dear Orestes as a light in the house! […] That Orestes may come here through some fortune is my prayer to you; and you must hear me, father! Grant me also to be much more chaste than my mother, and my hands to have greater piety." (129-131, 138-141)
Here, Electra prays to the spirit of her father Agamemnon to make Orestes come avenge him. She also prays for Agamemnon to help her play a more traditional female role within the household; unlike her mother, Electra wants to obey stricter sexual morality, and avoiding harming others impiously.