Necking is good for kissing, not singing...
Singers! When the neck is tight while singing most often times we are baring down to create stability, and often a darker color, or manufactured vibrato. Also tension in the neck will “crush” the larynx and also trap the sound without allowing true resonance. Tension of the neck is using muscles to engage, (frequently the head voice, sometimes chest), without truly releasing the larynx and getting to a smaller edge of the cord while in the spinning head voice behind the eyes masque and upper pharynx.
To avoid tension in the neck while singing one must get in a true supported breath line, and fully adducted cords that are engaged and working. Also, Jesse Norman is very very correct - stand up straight! Neck tension is used in connection with sending too much air through the cords to create sound. The throat is in a locked and gripped position and in an attempt to unlock the neck is employed. This does not make sense. The head must sit on top of the neck, aligned with the spine and posture. Tensing, neck and shoulders to muster out the sound is counter productive, and against the nature of vocal technique. One must allow the voice to zip up on the smaller edge and lengthening tilt of the cord, coupled with breath control, and trust that focused sound will have more ping and resonance. Neck tension is often when the singer is listening to themselves, instead of feeling the sensations, you will sound louder to you, but chances are the sound will not travel. Free the sound by allowing the instrument to work, and allowing the neck to unlock. Also if the neck is tense in the chest voice it is because the singer is beefing the sound and adding unnatural heft. For the lower fuller sound find more release of the larynx, and more resonance in the chest from a free supported more natural sound. Allow the body to stand in a slight pliee while singing to feel that the alignment and support is down not locked from a tight neck. Check that the shoulders are also not tight - envision that the shoulders are aiming towards the east and west. Trust that your notes will emerge because of the freedom, the notes will not emerge from the lock-down! Think of the diaphragm as 360 degrees, find breath throughout the wide circle of your body, the breath must flow, in a measured fashion (controlled from below the navel), with ease (no upper ab tension) - tensing the neck will not allow this. This round 360 feeling will also not allow the larynx to be hiked up or pushed overly down, just let the larynx be - but do think of a slight release or a slight feeling of slight down on the inhale and then “just” leave it there, yes it will move (and tilt!) some but you don’t need to attack the larynx to create your high or low tones.
While warming up and doing your vocalises/exercises incorporate some slight side to side head movements, also bend the top side of the head to the right, and the other top side of the head to the left, do this to free - you will feel tension leaving the neck, and also the shoulders and upper back. Keep the body aligned but do these slight side to side and semi-circular movements. Also while not singing, turn the head to the side, first left then center then right, 12 times each side, then do small front circles - 12 times, then do top of head to right and top of head to left 12 times each side, this will strengthen the neck and muscles around it. Often neck tension is due to tight alignment or weak alignment, and also processing the support and needed tension (not tenseness) in the breath line but placing it in the neck muscles and not in the support/breathing muscles. Also, make sure that your chin is not overly tucked or raised whether in high, middle or low voice. Let the chin float - do not shove down, or wrench up. The jaw should feel relaxed and hinged, not jutted forward. The back of the neck should feel long and the front of the neck slightly shorter. Allow the nuchal muscles of the back of the head to help the alignment but not feel tension to support the sound. Often neck, head, and tongue tension is just to grip the larynx and manipulate the sound rather than trusting the freedom of the sound and instrument to emerge, trust that your instrument will work for you, without force! Enjoy!