+1 to thinking in intervals. Steve Vai does a lot of interval type things. For example there is a 5ths lick he uses fairly often.
I want to make a couple points
1) Vai has spent hours composing and working out new ideas and then memorizing them and perfecting them. Most of the amazing licks you hear are not out of the blue. He has learned them before.
2) It sounds like you may want to learn a little bit about music theory. You hear what you want, but you don't know how to get them. learning what you are hearing may help. Start with intervals, learn what they are and learn to identify them by ear.
3) Be persistent. You will learn how to do it eventually.
I disagree with point number 2, because i am the inventor of unknown better and definitive new music theory so my tip is: don't try and learn because they all are wrong! sorry i'm not publishing althought i finished the new music rules in '98, probably it'l be afterdeath.