。、。
So she pulled up alongside, opened the window, and gave the horn a quick tap to let us know she was there.
Literal
She [topic-は] therefore this-side [to-に] approached. Window [object-を] open [and-て], herself [subject-が] there [in-に] is [thing-という] [in-に] notice [for me-てもらう] [in order to-ために] horn [object-を] lightly sounded.
A two-sentence narrative chunk packed with grammar. それゆえに ('therefore, for that reason') is a formal/literary connector, slightly stiffer than だから or なので. クラクション ('car horn') is a loanword — and an unusual one: it comes from the English brand name 'Klaxon' (an early electric horn manufacturer), rather than from a generic English word. The complex purpose clause 自分がそこにいるということに気づいてもらうために unpacks as: 自分がそこにいるということ ('the fact that she was there') + に + 気づいてもらう ('have (us) notice') + ために ('in order to'). The benefactive ~てもらう makes 'us' (the speaker's group) the noticing party doing the favor of perceiving her. 軽く ('lightly') is the adverbial form of 軽い ('light'), and 鳴らす is the transitive 'to sound' (paired with intransitive 鳴る 'to ring').