(12) Having many things to write unto you, I would not write with paper and ink: but I trust to come unto you, and speak face to face, that our joy may be full.
Having many things to write to you…
This letter is extremely short. Here, at the end of the letter, John is saying there are several things he could have added to the letter.
I’m not willing to write them with paper and ink
Another way of saying this is that there were many things he could have added, but he didn’t want to write them. The reason for this is made quite clear when he says he wants to come speak to them face-to-face. There are some things much better said face-to-face instead of in a letter.
But I trust that I will come to you and speak face to face
When you speak face-to-face with someone, as opposed to through a letter (or text message, or email, or some other written form of communication), it shows you care. Also, in person your tone, body language, and emphasis comes through. John may have had something very unpleasant things to say to them (see 3 John 9-10). John may have needed to talk to them about some things difficult to understand (see 2 Peter 3:15-16). He may have needed to have a discussion with them, to ask them questions and understand some things going on there. All of these things are much easier to do in person than by letter.
John had confidence, trust, he would be able to come see them. It is certain John prayed about it (James 4:15). We should follow the same example.
So that our joy may be full
The purpose of John’s planned face-to-face visit was to bring joy to them and to himself. We are given a clue in verse 4 about this. John rejoiced that the Christians were walking in truth. However, he didn’t say “all” of the Christians were walking in truth. Some of them were, but others were not. His plan was to go visit them, and possibly bring the wayward back to Christ. This would cause him great joy, but also bring great joy to the congregation as well. John’s joy always seems to center on the truth being followed (see also 1 John 1:1-4, especially verse 4).
(13) The children of thy elect sister greet thee. Amen.
The children of your elect sister greet you.
Since the “elect lady” of verse 1 is the church (perhaps specifically the congregation in Jerusalem), the “elect sister” would be the congregation where John was. Her children would be the members of that congregation.
They all send their greetings. This is the same word translated “salute” in Romans 16:16 (the churches of Christ salute you). It is more than just saying “hi.” It’s a greeting of friendship and fellowship.
This means “so be it,” or “I agree.” However, it is also used at the end of some of the Biblical letters to bring the letter to a close. It is a final re-emphasis of what’s been said, and showing John meant all of it.