Do Full Preterists believe that the perfect came and the gifts of the Spirit ceased in A.D. 70, as per 1 Corinthians 13:8-12?

It is not clear what percentage of full-preterists view the 'perfect' St. Paul is referring to here as events around AD 70. It is difficult to find significant full-preterist commentary on this particular passage.

My natural reading of 1 Corinthians 13:8-12, and my best guess, is that St. Paul is referring to Heaven. In Heaven, it seems natural to say we see God 'face to face', as described in 13:12.

Along these lines, some full-preterists understand the resurrection as being, first, the righteous dead in Hades being raised to Heaven in 'spiritual bodies' (see 1 Corinthians 15:44-49) around AD 70, and then secondly, the righteous on an on-going basis dying and being resurrected into Heaven immediately in spiritual bodies. Consider 1 Thessalonians 4:15-17,

"According to the Lord’s word, we tell you that we who are still alive, who are left until the coming of the Lord, will certainly not precede those who have fallen asleep. 16 For the Lord himself will come down from heaven, with a loud command, with the voice of the archangel and with the trumpet call of God, and the dead in Christ will rise first. 17 After that, we who are still alive and are left will be caught up together with them in the clouds to meet the Lord in the air. And so we will be with the Lord forever."

For an example of a full-preterist who holds this view, see If All End Time Prophecies are Fulfilled How is 1 Corinthians 13:9-12 Fulfilled?

"this unveiled “face to face” encounter also points to a literal face to face fellowship with Christ in heaven at the resurrection"

For an expansion on the idea of a resurrection from Hades and then immediate resurrection after death, see the same author's 1 Corinthians 15:50-54: A Preterist Commentary.

(This differs from, say, the Catholic view, which holds similarly that the dead have already been raised from Hades to Heaven, and then people after death are raised to Heaven on an on-going basis, but that this does not involve bodies and there will be another, and this time bodily, resurrection at Jesus' Second Coming.)

So on the full-preterist view described above, the resurrection has happened and is now on-going, and people in Heaven have spiritual bodies. On the view that St. Paul's 'the perfect' refers to Heaven-the resurrection, just as we are 'as angels' and do not marry in the resurrection (Matthew 22:30), also we do not speak in tongues, prophesy, or have 'knowledge' in the resurrection-Heaven, in the senses St. Paul means of these words here. This makes sense to me - once in Heaven, what is the purpose of speaking in tongues, for example?

So this view - that 'the perfect' refers to a Heavenly resurrection which is future for Christians here on Earth - can be agnostic about whether these specific gifts have ceased.

(You could also argue that this view isn't technically 'full-preterist', but I will leave that debate aside.)

However, some full-preterists see the 'perfect' here as describing the full coming about of the New Covenant, and tie the resurrection to only a covenantal resurrection (a 'corporate' resurrection of God's people - Israel was dead, and then was 'resurrected' with the full establishment of the new covenant). This view entails cessationism, as the covenantal resurrection has already happened and the 'perfect' applies to current Christians on Earth.

One full-preterist who holds this view is Michael Sullivan, and he discusses this at length in Tongues, Prophecy and Knowledge "Ceased" in AD 70 – A Study of "That Which is Perfect" (1 Cor. 13:8-12).

"“that which is perfect” and the “face to face” “knowledge” of 1 Corinthians 13:10-12, are references to Christ’s return and the arrival of the new heavens and earth by AD 70[.]"

It is not clear to me exactly how someone like Michael Sullivan would explain apparent manifestations of tongues, prophecy, and knowledge. He believes that at least most instances of 'tongues' nowadays are what appears to be 'gibberish', unlike what Acts is apparently talking about on Pentecost, most 'prophecy' is vague, and more akin to a typical horoscope, and similarly with knowledge (see his remarks at the 1:37:00 mark of Did Prophecy, Tongues & Knowledge Cease in AD 70?).

However, it is possible someone like Sullivan could also make a distinction between these as gifts an individual possesses (gifts he would hold do not happen anymore) and the miraculous occurrences which involve these sorts of things (and so could happen).

Having said that, full-preterists who are cessationists probably have similar views in general on responses to apparent instances of gifts of tongues, prophecy, and knowledge as cessationists more broadly. There will be some background theological differences (all Biblical prophecy has been fulfilled), but my guess is in terms of responding to particular apparent instances, the response will be similar to cessationists in general.