Conviction does not only come by the Holy Spirit throughout the Bible. Look at the OT: the Holy Spirit did not personally and permanently indwell anyone, yet some people were considered "righteous" in God's eyes. How could this be? The answer is that we in the church age are in a very unique situation. No one before or after this particular age was or will be personally and permanently indwelt by the Holy Spirit.
Revelation tells us how drawing/witnessing/evangelism will be done: the 144,000 of Israel who believe after the antichrist comes to power, the "flying eagle", and the angel (see that link in the earlier post on Revelation for details). Even now, along with the work of the Spirit, we are told in the Bible that "faith comes by HEARING, and hearing by the WORD OF GOD", so it is no mystery as to how people will know how to be saved during the Tribulation.
Notice in Revelation during the worst of the plagues and judgments, that people "refuse to repent" even though they know it is GOD who is judging them. People understand what's happening and why, so you might say that even judgment is a form of God's "drawing". He never leaves himself without a witness. Remember also that while Jesus was on the cross, he said "My God, my God, why have you forsaken me?". That was an instance of not only the Holy Spirit being gone for a time, but is the only instance where even the Father turned away. But during the Tribulation, at least the Father is watching.
Overall, just remember not to mix apples and oranges, the OT and the NT, Israel and the Church. There are other documents referred to in the one on Daniel, which would help spell out these things in more detail (some are in my blog here). We live in the age of Faith, not sight, but during the Tribulation people will have more "sight" than they ever wanted.