catch up with the eclipse prayer in the second rukoo’ of the first rak’ah

Praise be to Allah.

The rak’ah will count in Salat al-Kusoof if you catch up with the first rukoo’. Based on what you say in your question, you caught up with the second rak’ah only, so after the imaam says the salaam, you have to do a whole rak’ah with its two recitations, two rak’ahs and two sujoods.

(See the description of Salat al-Kusoof, Question# 210590  ).