Revelation has always been progressive, and it is never until God gives understanding of the revelation that we can actually incorporate that into how we understand any particular passage of Scripture and its particular context. A good example of this is seen in the understanding of the disciples of Christ prior to Pentecost. The revelation available to them did indeed have numerous prophecies which, unless we keep revelation in context, would make us wonder why it is we see such ignorance on their parts concerning Christ. I mean, hadn't they ever read Isaiah 53 for example?
The key to placing this particular issue in its proper context is understanding that the Mystery of Christ had not been revealed to them and it would not be until the Spirit of God came in the particular ministry of Comforter. This brings us back to the question you asked. The Trinity is not found in explicit teaching, however, certain doctrines rely on implicit teaching. I will give one example of the Trinity implicitly taught by none other than Christ Himself:
John 14:15-23 KJV
15 If ye love me, keep my commandments.
16 And I will pray the Father, and he shall give you another Comforter, that he may abide with you for ever;
I would first point out that Christ is the Comforter contrasted to the Comforter that will come. He was meant to be for the consolation of Israel. The promise given here is that while Christ stated He had to depart (John 16:7), another Comforter would come and He, not it, would be with them (the disciples) forever. Remember their hearts were sorrowful because of His departure.
17 Even the Spirit of truth; whom the world cannot receive, because it seeth him not, neither knoweth him: but ye know him; for he dwelleth with you, and shall be in you.
Here we see the Comforter, the Spirit of Truth, was already with them (the Spirit of God has always ministered in and through men, and had empowered them for ministries such as Prophet, Priest, King, and Warrior (known as the Filling of the Spirit of God)), but would, at a future time...be in them.
Now we see that not only will the Comforter come to be in them forever, but...
18 I will not leave you comfortless: I will come to you.
...Christ, the Son of the Living God would also come to them.
So far we see the Son and the Spirit, Both coming to the disciples.
19 Yet a little while, and the world seeth me no more; but ye see me: because I live, ye shall live also.
20 At that day ye shall know that I am in my Father, and ye in me, and I in you.
At that day-or in other words, in the future-the disciples would know (and this is the understanding that God would give them when the Mystery of Christ is revealed) that Jesus Christ is in (not with, though that is true as well) the Father, and the disciples in He (Jesus Christ), and Jesus Christ in the disciples.
I would ask you to consider at this point the state of the disciples at this time, just after the "last supper." Were the disciples in Christ at this time? No. This is precisely what Christ is stating will take place when the Comforter comes. And...when He comes.
21 He that hath my commandments, and keepeth them, he it is that loveth me: and he that loveth me shall be loved of my Father, and I will love him, and will manifest myself to him.
22 Judas saith unto him, not Iscariot, Lord, how is it that thou wilt manifest thyself unto us, and not unto the world?
23 Jesus answered and said unto him, If a man love me, he will keep my words: and my Father will love him, and we will come unto him, and make our abode with him.
Here we see that the Father is also said to be coming to abide in the disciples.
Now the question we ask is what does Scripture teach? Does it teach we are indwelt by the Father, Son, and Holy Ghost...
...or not?
This teaching clearly sets forth the Eternal Indwelling of the Father, Son, and Holy Ghost. The reason we can be indwelt by all Three is that God is One. One mistake people often make is failing to distinguish the Eternal Nature of the Son of God as opposed to the Christ having a beginning in time. That is...when God created the Body He would take up residence in for the purpose of Eternal Redemption...that He might reconcile Man unto Himself.
I will leave it at that and open this up for critique.
God bless.