How do proponents of Sola Scriptura address the ministry of those Apostles who authored no parts of Scripture?

Just as the political principle of separation of powers isn't needed and wouldn't make sense in an absolute monarchy or a dictatorship, so too does the doctrine of sola scriptura assume and require that there are actually other sources of divine inspiration alongside the scriptures. Sola scriptura is a doctrine that sets controls on how we understand and use other sources of divine inspiration.

So sola scriptura allows for other sources of divine special revelation, what is often called prophesy. Sola scriptura governs how we understand and use the spiritual gifts of prophecy and interpretation. (Note that many protestants are cessationist and would say the gift of prophecy has ceased; this doesn't change this aspect of sola scriptura as it applies equally to the prophecy of the apostolic age.) Sola scriptura says that when God inspires a prophet they will never say something contrary to the scriptures, and so our interpretations of their prophecies must always be in line with the scriptures. Sola scriptura also helps us have a healthy attitude towards prophecy: we do not trust self-proclaimed prophets blindly, but we test their words. Even when they are compatible with the scriptures we do not trust them as much as we trust the scriptures. If God continues to enable the spiritual gift of prophecy today, he does not do so with the intent that modern prophecies in any way supplant the scriptures. Extra-biblical prophecies will never be necessary, and they will always be secondary towards the scriptures he has inspired and preserved for all generations.

Similarly, sola scriptura governs the roles of tradition, reason, and wisdom in the church. We recognise that God's indwelling spirit enables us to reason well and gives us spiritual wisdom. We recognise the collective wisdom of groups of Christians, both now on a local context, and the collective wisdom of 2000 years of church history. All of these are valuable sources of knowledge that God has given us. But sola scriptura means that they all are always secondary to the scriptures. Just as God will never give us a prophecy that contradicts the scriptures, so he will never give us wisdom that contradicts the scriptures, nor preserve traditions for us that go against what he has recorded for us in the scriptures. But while there are a few traditions that protestants would say directly contradict the scriptures (for example, the sinlessness of Mary), most do not. For the rest, sola scriptura still governs our relationship to tradition, reason, and wisdom. Just as God's divine inspiration has guided the Christian church in the past leading us to certain understandings of the scriptures, so he continues to guide us now. Sola scriptura says there is no guarantee that any doctrine of the church is certain; the only mark of divine certainty is on the scriptures. So our relationship to the scriptures is one of an ongoing project of investigation guided by the spirit's insights. As God guides us we may collectively decide that some things which were believed in the past, although they do not directly contradict the scriptures, are weaker exegetically and have unfortunate theological implications compared to alternative interpretations. And just as we have a measure of skepticism towards earlier generations' traditions and interpretations, so future generations will judge that some of our interpretations and theological theories are unjustifiable as God continues to guide them. So for example, the perpetual virginity of Mary, despite going back to the early church, and despite being affirmed even by important protestant theologians including Luther, Cranmer, and John Wesley, is now rejected by the majority of protestants for both exegetical reasons and theological arguments and implications.

The controls of sola scriptura apply just as much to the original Twelve Apostles as they do in our age. God has always inspired more than just the scriptures. What sola scriptura teaches however is that the scriptures are the only inspired revelation that God intends for all Christians in all time to rely upon. The apostolic authority of the Twelve was to speak with inspiration as the church was initiated. Some of what they taught was preserved by God for us in the scriptures, but not all. We conclude that the things they said that were not preserved for us were not preserved because God does not will for us to have them, and that if we could somehow time travel back to hear the Apostles ourselves, what they said would still not be of equal authority to the scriptures, but to that of any other inspired prophecy. It is after all God who gives his authority to his inspired messages, and he is free to vary the authority he gives.

Finally, what John said in 2 John 12 and 3 John 13 does not imply any superiority of spoken inspiration over written inspiration, but reflects the many advantages that in-person ministry has over ministry by written correspondence.