This passage answers the question: "What shall we do, that we may perform the works of God?"
Is Jesus here defining the work of God in the appositional clause? Or is he delineating how one performs the work of God. The appositional clause could either identify (define) or explain the first nominal clause, and it seems to me that Jesus is giving a prescription in the latter part of 6:29, not a description. At least that is a possible reading of 6:29.
GRB Murray writes: "The hearers, as they were Jews, interpret 'the works which God demands' as works of the Law, which God will reward with eternal life. They learn, however, that the 'work' God wants is faith in the one God has sent" (John, 91).
Jn 6:29 seems to have some bearing on our understanding of Jn 17:3--and 6:29 appears to be prescriptive (i.e., it tells us what God expects or wills).
From the Greek Testament Critical Exegetical Commentary:
The meaning is not,—that faith is wrought in us by God, is the work of God; but that the truest way of working the work of God is to believe on Him whom He hath sent.
ἔργον, not ἔργα, because there is but this one, properly speaking, and all the rest are wrapt up in it (see James 1:25).