From the Roman Missal, Good Friday:
“18 For the Adoration of the Cross, first the Priest Celebrant alone approaches, with the chasuble and his shoes removed, if appropriate. Then the clergy, the lay ministers, and the faithful approach, moving as if in procession, …”.
“20. While the adoration of the Holy Cross is taking place, the antiphon … or other suitable chants are sung, during which all who have already adored the Cross remain seated.”
22. A cloth is spread on the altar, and a corporal and the Missal put in place. Meanwhile the Deacon, or if there is no Deacon, the Priest himself, putting on a humeral veil, brings the Blessed Sacrament back from the place of repose to the altar by a shorter route, while all stand in silence.”
In the Roman Missal used in Australia, the General Instruction of the Roman Missal, n. 43, has a special instruction. “In Australia: …They are to kneel again after the Agnus Dei (Lamb of God) until the distribution of Holy Communion. During the period of sacred silence after Communion, they may either sit or kneel.”
For this Good Friday ceremony there is no Lamb of God. So there is no cue to kneel. So remaining standing seems correct to me, at least in Australia.