John 14:16: "'And I will ask the Father, and he will give you another Helper, to be with you forever'"
John 14:26: "'But the Helper, the Holy Spirit, whom the Father will send in my name, he will teach you all things and bring to your remembrance all that I have said to you.'"
Romans 8:5-11: "5 For those who live according to the flesh set their minds on the things of the flesh, but those who live according to the Spirit set their minds on the things of the Spirit. 6 For to set the mind on the flesh is death, but to sent the mind on the Spirit is life and peace. 7 For the mind that is set on the flesh is hostile to God, for it does not submit to God's law; indeed it cannot. 8 Those who are in the flesh cannot please God.
"9 You, however, are not in the flesh but in the Spirit, if in fact the Spirit of God dwells in you. Anyone who does not have the Spirit of Christ does not belong to him. 10 But if Christ is in you, although the body is dead because of sin, the Spirit is life because of righteousness. 11 If the Spirit of him who raised Jesus from the dead dwells in you, he who raised Christ Jesus from the dead will also give life to your mortal bodies through his Spirit who dwells in you."
Titus 3:5-7: "5 he saved us, not because of works done by us in righteousness, but according to his own mercy, by the washing of regeneration and renewal of the Holy Spirit, 6 whom he poured out on us richly through Jesus Christ our Savior, 7 so that being justified by his grace we might become heirs according to the hope of eternal life."
1 Corinthians 2:10-16: "10 these things God has revealed to us through the Spirit. For the Spirit searches everything, even the depths of God. 11 For who knows a person's thoughts except the spirit of that person, which is in him? So also no one comprehends the thoughts of God except the Spirit of God. 12 Now we have received not the spirit of the world, but the Spirit who is from God, that we might understand the things freely given us by God. 13 And we impart this in words not taught by human wisdom but taught by the Spirit, interpreting spiritual truths to those who are spiritual.
"14 The natural person does not accept the things of the Spirit of God, for they are folly to him, and he is not able to understand them because they are spiritually discerned. 15 The spiritual person judges all things, but is himself to be judged by no one. 16 'For who has understood the mind of the Lord so as to instruct him?' But we have the mind of Christ."
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The text is public domain. #498 and #499 are the same except for an "Amen" at the end of #499.
Come, Holy Ghost, Creator blest,
And make our hearts Your place of rest;
Come with Your grace and heav'nly aid,
And fill the hearts which You have made.
To You, the Counselor, we cry,
To You, the gift of God Most High;
The fount of life, the fire of love,
The soul's anointing from above.
In You, with graces sevenfold,
We God's almighty hand behold
While You with tongues of fire proclaim
To all the world His holy name.
Your life to ev'ry thought impart,
And shed Your love in ev'ry heart;
The weakness of our mortal state
With deathless might invigorate.
Drive far away our wily foe,
And Your abiding peace bestow;
With You as our protecting guide,
No evil can with us abide.
Teach us to know the Father, Son,
And You, from both, as Three in One
That we Your name may ever bless
And in our lives the truth confess.
Praise we the Father and the Son
And Holy Spirit, with them One,
And may the Son on us bestow
The gifts that from the Spirit flow!
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The fourth verse, particularly the lines "The weakness of our mortal state / With deathless might invigorate," comes from Romans 8:5-11.
The fifth verse seems to come from Titus 3:5-7. The hymn seems to render "by the washing of regeneration and renewal of the Holy Spirit" as "With You as our protecting guide, / No evil can with us abide."
The first half of the sixth verse ("Teach us to know the Father, Son, / And You, from both, as Three in One") could come from either John 14:26 or 2 Corinthians 2:10-16. Both of those passages name the Holy Spirit as a teacher, but the 2 Corinthians text is much more detailed.
John 14:16, 26 seem to appear at the very end, in the lines "And may the Son on us bestow / The gifts that from the Spirit flow!" but the beginning two verses of the hymn call upon the Spirit with faith and confidence in these words of Christ, so these passages could be cited there too.
The lines "While You with tongues of fire proclaim / To all the world His holy name" in the third verse is a reference to Acts 2:1-13.