Parakletos in Scripture
The Greek term is παράκλητος which if transliterated would be parakletos. This word is only used four times in John's Gospel and once in First John. It is not used in the LXX.
John 14:16:17a DRA
And I will ask the Father, and he shall give you another Paraclete, that he may abide with you for ever. The spirit of truth...
John 14:26 DRA
But the Paraclete, the Holy Ghost, whom the Father will send in my name, he will teach you all things, and bring all things to your mind, whatsoever I shall have said to you.
John 15:26 DRA
But when the Paraclete cometh, whom I will send you from the Father, the Spirit of truth, who proceedeth from the Father, he shall give testimony of me.
John 16:7 DRA
But I tell you the truth: it is expedient to you that I go: for if I go not, the Paraclete will not come to you; but if I go, I will send him to you.
1 John 2:1 DRA
My little children, these things I write to you, that you may not sin. But if any man sin, we have an advocate with the Father, Jesus Christ the just
After rendering παράκλητος consistently as parakletos in the Gospel, the Douay-Rheims translators opted to translate it as advocate in First John.
The first use is without the article; instead it is identified as ἄλλον παράκλητον which would be transliterated as allos parakletos. The remaining uses in the Gospel are with the article, ὁ παράκλητος. This pattern indicates the article is anaphoric, meaning ὁ παράκλητος is ἄλλον παράκλητον first mentioned in 14:16. Therefore, in the Gospel, the parakletos is allos parakletos. The use in First John is without the article.
Allos Parakletos
When Jesus first tells the disciples about parakeltos, He informs them it will be allos, which is understood as another. Obviously, in order to send another parakeltos, a first parakeltos must have been sent. Even if First John did not specifically identify Jesus as the first parakletos sent, the Gospel not only implies this, but logically, who else but Jesus could be the first parakeltos?
Essentially, First John gives the meaning of parakletos. It is one who acts on behalf of the sinner with the Father. The One who gave His life as a ransom; the One who came to take away the sin of the world; this same One now acts on behalf of the sinner with the Father. Only Jesus qualifies the first parakletos.
Jesus is parakletos and allos parakeltos is the Spirit of the Truth. Jesus was the first parakletos; the Spirit of the Truth is allos parakeltos. When first identifying the Spirit of the Truth, Jesus could have omitted allos, or Jesus could have said the parakletos, or Jesus could have said heteros parakletos. Heteros parakeltos would also be understood as "another" parakeltos. The difference between allos and heteros is the first is another of the same type; the second is another of a different type.
By identifying the Spirit of the Truth as allos not heteros or the, Jesus is stating the Spirit of Truth is another like Himself and is not different from Himself. By not using the article with either the Spirit of Truth or with Jesus Christ the Just, these texts demonstrate equality between parakletos and allos parakeltos. That is, neither may rightly be called the parakeltos, since both were sent and both are parakeltos. The only difference is one was sent before the other, and, obviously, the one who was sent first, is still parakeltos.
Conclusion
The language used states unequivocally Jesus was the first parakeltos sent to mankind. In the Gospel, Jesus describes the Spirit of the Truth as another like Himself.
If the Spirit of Truth was different from Jesus, then He should have said heteros not allos. In other words, by choosing allos not heteros, Jesus was stating the Spirit of the Truth was a parakletos exactly like Himself.