I realize that the Eucharist is taken for the first time at Easter Vigil, but is it continued for candidates of RCIA through Confirmation, or is it a received for the second time at confirmation?
RCIA candidates who receive the sacraments of Baptism and First Eucharist at the Easter Vigil Mass also receive Confirmation at that time:
Today in all the rites, Latin and Eastern, the Christian initiation of adults begins with their entry into the catechumenate and reaches its culmination in a single celebration of the three sacraments of initiation: Baptism, Confirmation, and the Eucharist.
(Catechism of the Catholic Church, paragraph 1233)
The Code of Canon Law confirms this:
Unless there is a grave reason to the contrary, an adult who is baptized is to be confirmed immediately after baptism and is to participate in the eucharistic celebration also by receiving communion.
In turn, this approach laid out by the Canons and the Catechism is meant to support what appears in the Second Vatican Council's Ad Gentes Decree on the Missionary Activity of the Church:
Then, when the sacraments of Christian initiation have freed them from the power of darkness (cf. Col. 1:13), having died with Christ been buried with Him and risen together with Him (cf. Rom. 6:4-11; Col. 2:12-13; 1 Peter 3:21-22; Mark 16:16), they receive the Spirit (cf. 1 Thess. 3:5-7; Acts 8:14-17) of adoption of sons and celebrate the remembrance of the Lord's death and resurrection together with the whole People of God.
(Ad Gentes section 14)
Thus, there is no continuance through Confirmation, since there is no delay of Confirmation.