That towel move is a real physical therapy technique called a self SNAG, and the speed of the relief tells you something most people never learn about their own neck. Muscle tissue takes weeks of loading to actually lengthen. So when stiffness vanishes in a few seconds, the muscle was never what changed.
What changed is the signal your brain was sending to it.
The small facet joints stacked down the back of your neck sit at roughly a 45 degree angle. When one of them gets irritated or stops gliding smoothly, your brain protects it by clamping down the surrounding muscles. That clamp is the stiffness you feel. The tissue underneath is usually fine, it's just being held under orders.
The towel edge hooks under one vertebra. When you pull forward and up along that 45 degree joint plane while turning your head, you glide the joint through the exact motion it was refusing, with support the whole way. Your brain gets live evidence the movement is safe and drops the clamp. Physical therapists do the same glide with their thumbs and call it a SNAG, short for sustained natural apophyseal glide. Brian Mulligan, the New Zealand physio who developed the method in the 1980s, designed the towel version specifically so patients could run it on themselves at home.
Which is why years of stretching can lose to thirty seconds with a towel. A stretch tries to overpower the brain's grip. A glide convinces it to let go.