Napr. nejako takto (netestované):

function initAnchors(anchor1, anchor2) {
  anchor1.onmouseover = function() {
    anchor2.style.backgroundColor = "red";
    // alebo: anchor2.className += " hover";
  };

  anchor1.onmouseout = function() {
    anchor2.style.backgroundColor = "";
    // alebo: anchor2.className = anchor2.className.replace(/(^|\s+)hover(\s+|$)/, " ");
  }
}

window.onload = function() {
  initAnchors(
    document.getElementById("id-prveho-odkazu"),
    document.getElementById("id-druheho-odkazu"));
}