I get asked about horizontal lines on the neck and the formation of loose thin wrinkly skin on the neck a fair amount. Botox does not help horizontal lines on the neck.
Some people have horizontal neck lines since they were young. It is just a variant that some people possess. As we age, the skin in our neck becomes thinner and looses its support. This tends to exacerbate these lines as well. This issue is a skin issue, not a muscle issue. Botox affects muscular activity and can be used in the neck for neck bands, which are vertical lines on the neck.
So what can help? Well, a neck lift will pull the neck skin tighter and make the skin seem firmer and with more support, but it might not eliminate the horizontal neck lines completely. Using fillers directly into the lines can help improve them as well. Using lasers or creams might help in making the skin a bit more swollen, and hence appear thicker and more supple. This might improve the appearance of the skin, but will need to be made part of your routine and be done on a regular basis.