If that style comes from a CSS file, you'll have to search for it in document.styleSheets, which will be messy.
If you are open to dynamically creating a element containing that CSS instead, you can modify it programmatically.
var slidingTagLiAfterStyle = document.createElement("style");
slidingTagLiAfterStyle.innerHTML =
".slidingTag li:after {
content: '';
z-index: 3;
height: 6px;
}";
document.head.appendChild(slidingTagLiAfterStyle);
...
slidingTagLiAfterStyle.innerHTML = slidingTagLiAfterStyle.innerHTML.replace(/height: [0-9]+px/, "height: 12px"); // or whatever you want to set it to