Let's simplify this.
#1 Check out this video by Paul Mckay. This video in particular, helped me simplify the idea of vocal runs.
#2 Practice your scales. The better you know what notes sit between each octave, the easier you can hear/sing them! This can be as simple as sitting at a piano or following a vocal program with prompts.
#3 Break down the vocal run. Slow down and identify each note. Then slowly speed it back up to the proper tempo. If it's still sloppy, go back to the tempo where you could sing the run most clearly. You'll be surprised how quickly you'll pick this skill up.
#4 Practice the run on an EEE vowel. If the run is on a "you" try singing "YEW" instead. This will help stabilise the palate and get you in your vocal mask.
#5 Focus the air through the top teeth. This focuses the sound in the vocal mask and lifts some particular vocal mechanisms you need in order to sing quickly but accurately. You need air to sing, you need air placement to sing runs.
#6 Focus everything forward. From body positioning to sound placement. Use your finger to point the notes forward. Using your hands while learning newer singing skills is so helpful because physical motion helps propel vocal motion.
If you want more, you can book an online vocal lesson with me!
Questions? Comment below!
See you soon + stay warm! Cx