So if Jesus is the perfect in 1co 13....
The perfect is neuter gender when looking at the Greek.. it is a 'thing' or 'that' .. relating to something inanimate.
Also.. whatever is in part in 1co 13 is completed by the perfect.
So the perfect would be a completion of prophecy, tongues and knowledge..which are all ties to the progressing revelation of scripture at the time.
Now.. following this though is the seeing 'face to face ' .. which can be interpreted either way to be about Jesus or scripture..
So 1 co 13 doesn't stand alone and is supported by the likes of Ephesians 4 and other scripture.
Added to this is the experience of what people are calling tongues and prophecy compared to what the guidelines set down by Paul are and the case for at least sign gifts finished is strong.
"when that which is perfect is come" is when we are in that state of resurrection. When we see him face to face and are like him. We will know as we are known.
That which is perfect according to Paul was when he would attain the resurrected state which he called being made perfect in Philippians. 3
He said he was not already perfect but he pressed on toward that goal and would achieve it when he had obtained the resurrection from the dead. Now since Paul called that being perfect we can apply that to his statement in 1 Cor 13 that Paul considered "that which is perfect is come" as that STATE which he will obtain post resurrection and in that day he would know fully and not in part and have that face to face communion with Christ and no longer need the gifts like prophesy or tongues and interpretation of tongues, or these other gifts like words of knowledge. This state of perfection is still future for all of us.
Philippians 3
10My goal is to know him and the power of his resurrection and the fellowship of his sufferings, being conformed to his death,
11assuming that I will somehow reach the resurrection from among the dead.
12Not that I have already reached the goal or am already perfect, but I make every effort to take hold of it because I also have been taken hold of by Christ Jesus.
1 Cor 13:
But as for prophecies, they will come to an end; as for tongues, they will cease; as for knowledge, it will come to an end.
9For we know in part, and we prophesy in part,
10but when the perfect comes, the partial will come to an end.
12For now we see only a reflection as in a mirror, but then face to face. Now I know in part, but then I will know fully, as I am fully known.
In another scripture it compares reading the word as looking into a mirror. So the written word that we read acts like a mirror showing us what we look like (which isn't always pretty) and showing us what we should strive for. Perfection is our goal and that cannot be obtained until the resurrection. At that time we will not need these gifts. At that time they will cease.
"That which is perfect" reference by Paul in 1 Cor 13 is not Jesus or Scripture, it is our state of being post resurrection. What we will be in that day as it relates to our knowledge.