Should vocal harmony follow functional harmony rules?
Like I-V-I thing?
What are some techniques to make vocal harmony resolve and sound like a phrase instead of random chords?!

 

That's just it: I'm not really sure harmonies ever "resolve", or even need to, do they?
I suppose it's contextual, as everything is.
Harmony is harmony, vocal or instrumental.
There are different harmonization theories, not just functional harmony, and they are all applicable.
Perhaps re-listen to John & Paul's 2 part stuff.

Uh, that one's on you lol!

 

While I believe harmony rules should follow music and you can do whatever sounds right, if you want some rules to follow, check Palestrina-style renaissance counterpoint.

Edit: Or try this

 

Last edited: Dec 8, 2019

You can try something like this:



This is a I-ii7-I-V7-I, and it's the same cadence on all Hanon scales, major or minor.
I'm a bit rusty in harmony, but with a little refresh I could explain the rules behind this and how rebuild it in all scales without reading the score.