Are there other passages that state, implicitly or explicitly, that the believer is indwelt by the Father and/or the Son?
A couple of texts in the Gospel of John seem to say the same thing as Colossians 1:27 - John 14:20; 15:4. 2 Corinthians 13:5 would also apply.
John 17:23 may indicate both the Father and the Son’s indwelling the believer:
17:20 "I am not praying only on their behalf, but also on behalf of those who believe in me through their testimony, 17:21 that they may all be one, just as you, Father, are in me and I am in you. I pray that they may be in us, so that the world may believe that you sent me. 17:22 The glory you gave to me I have given to them, that they may be one just as we are one-- 17:23 I in them and you in me--that they may be completely one, so that the world may know that you sent me, and you have loved them just as you have loved me.
If the Father indwells the Son, and the Son indwells the saint, then both Father and Son indwell the believer, along with the Spirit. I would think that because the Father, Son, and Holy Spirit are one, the indwelling of the Holy Spirit would imply the indwelling of the entire Godhead.
1 John 4:4 may also support the fact that God indwells the believer.
4:4 You are from God, little children, and have conquered them, because the one who is in you is greater than the one who is in the world.
If we are “from God,” then when John writes “the one who is in you,” in the same verse he could be referring to God.
Note also these verses in 1 John 4:
4:11 Dear friends, if God so loved us, then we also ought to love one another. 4:12 No one has seen God at any time. If we love one another, God resides in us, and his love is perfected in us. 4:13 By this we know that we reside in God and he in us: in that he has given us of his Spirit. 4:14 And we have seen and testify that the Father has sent the Son to be the Savior of the world. 4:15 If anyone confesses that Jesus is the Son of God, God resides in him and he in God (1 John 4:11-15).