Here is the rubric regarding eucharistic adoration on Holy Thursday night/Good Friday morning from Paschale Solemnitatis:
The Blessed Sacrament should be reserved in a closed tabernacle or pyx. Under no circumstances may it be exposed in a monstrance… (PS 55).
After the Mass of the Lord’s Supper [on Holy Thursday], the faithful should be encouraged to spend a suitable period of time during the night in the church in adoration before the Blessed Sacrament that has been solemnly reserved. Where appropriate, this prolonged eucharistic adoration may be accompanied by the reading of some part of the Gospel of Saint John (ch. 13-17).
From midnight onward, however, the adoration should be made without external solemnity, for the day of the Lord’s Passion has begun (PS 56).
So, while prolonged eucharistic adoration of the reserved (not exposed) Blessed Sacrament into the early morning hours of Good Friday is permitted, after midnight it should be silent adoration. When the adoration should end is not clearly defined by the document, but the wording of the rubric seems to indicate that the adoration should take place during nighttime hours (e.g., “the faithful should be encouraged to spend a suitable period of time during the night in the church in adoration”; emphasis added).