Learn Hardcore Korean: yaksogeul kkamppakhaesseoyo.

약속 can mean both “promise” and “appointment/plan to meet.” Context decides. In everyday speech, it often covers both. For a restaurant booking or a doctor’s slot specifically, Koreans also say 예약 (reservation), e.g., 치과 예약.

Why is it 을 after 약속 and not 를?

을/를 is the object marker. You use 을 after a noun ending in a consonant and 를 after a noun ending in a vowel. 약속 ends with ㄱ, so it’s 약속을.

Can I drop the object particle and just say 약속 깜빡했어요?

Yes. In casual or fast speech, object particles are often omitted: 약속 깜빡했어요. Keeping it (약속을) is never wrong and is more careful/clear.

Why is it in the past tense (했어요) instead of present (해요)?

Forgetting is a completed event, so Koreans naturally use the past: 깜빡했어요. Present (깜빡해요) would sound odd unless describing a habitual tendency (“I tend to forget”).

What nuance does 깜빡하다 have compared to 잊다, 잊어버리다, and 까먹다?

깜빡하다: a momentary lapse—“it slipped my mind.” Mild, apologetic.
잊다: neutral “to forget,” common in writing or careful speech (약속을 잊었어요).
잊어버리다: “forget completely/by accident,” adds a sense of finality or regret.
까먹다: very colloquial/slangy “to forget,” can feel blunt or rude in formal contexts.

Is 깜빡 a separate word or part of a verb?