you would think there would be something to confirm this?
There are two confirmations of sorts - of this, or two witnesses, if you want to put it that way.
I have never run into the term 'Cessationist' before. It is a convenient term if all know it. Since you described what your subject was, I understood its reference. If the subject had been different, I wouldn't have; I would have thought it had to do with California leaving the US and becoming a country.
While scripture doesn't give us a lot of information, there is the following:
Acts 8:18: ASV: Now when Simon saw that through the laying on of the apostles’ hands the Holy Spirit was given. . .
2 Timothy 1: 6 For which cause I put thee in remembrance that thou stir up the gift of God, which is in thee through the laying on of my hands.
Acts 19: 6 And Paul laying hands on them, the Holy Spirit came on them, and they spoke in languages and prophesied.
The teaching here is implicit and specific.
The Apostles, the twelve, and Paul appointed specifically by Christ himself, had the authority to pass on the gift of the Holy Spirit by means of the laying of hands on a person when done with this purpose in mind. It wasn't just any touch from Paul that passed this on btw. Otherwise all manners of unbaptized people might be getting the gift.
If then the Apostles had this gift, as it clearly tells us it was restricted to, the death of the Apostles would mean that the gifts of the Holy Spirit done in this manner could no longer be passed on. The apostle John would then be the most likely last apostle who had this ability so that by perhaps 150CE all these gifts had passed away.
What needs to be taken into serious account is this:
1 Corinthians 12: 27 And you are Christ's body, and members in part. 28 And God placed some in the church: firstly apostles; secondly, prophets; thirdly, teachers; then works of power; then gifts of healing, helps, governings, kinds of languages. 29 Are all apostles? All prophets? All teachers? All workers of power? 30 Do all have gifts of healing? Do all speak languages? Do all interpret? 31 But zealously strive after the better gifts.
We first notice that the gifts of the HS were not given so that one individual would have them all; rather, it seems that each individual had his or her own gift, be it prophesying, healing, works of power (?), languages, interpreting.
What I especially think important for this discussion is the gift of healing. Why? Because if we look at Jesus and the apostles' healing, there were no obstacles to what was being healed. It was a full and complete healing, done mostly immediately, though at times, Jesus took a few minutes to talk a blind man through his healing. Nonetheless, there were no partial healings, no problems that could not be healed.
This kind of healing does not exist today.
The conclusion of the matter then is simple. We have the fact that the 'laying of hands from the apostles' bestowed these gifts, nobody else could bestow these gifts. Today, the healing is not what we see happening in the Bible. From this, we can conclude that the gifts have now passed into history. As it said,
1 Corinthians 13:8-10 says "Love never ends. As for prophecies, they will pass away; as for tongues, they will cease; as for knowledge, it will pass away. For we know in part and we prophesy in part, but when the perfect comes, the partial will pass away"
From this, we may conclude via Sola Scriptura and the present state of affairs - that it appears this has now transpired.