Extracted logic to strategies. Possible re-use. Easier to follow paths.

remove-wishlist-products-refactored.js

  static $wishlistList = $(".wishlist-list__body");
  static $myFavouritesRollover = $(".mini-favourites");
  static $myFavouritesSendList = $(".wishlist-send-list");
  static emptyWishlistHTML = $("#emptyWishlistPopupTemplate").html();
  static $wishlistCount = $("[data-wishlist-item-count]");	

  static $myFavouritesRolloverContainer = $(
    ".my-favourites-rollover__content",
    $myFavouritesRollover
  );
  static $myFavouritesRolloverControls = $(
    ".my-favourites-rollover__controls",
    $myFavouritesRollover
  );

static removeProductFromWishListHandlerRefactored(e) {
    const productRemovalStrategies = [];

    e.stopPropagation();
    const target = $(e.currentTarget);
    const productCode = target.data("product-code");

    const wishlistData = await requestPost("/favourites/remove", { productCode }, { format: "text" });
    const count = this.getCount(wishlistData);

    let strategyObject = {};
    strategyObject[count === 0] = this.emptyWishListStrategy;
    productRemovalStrategies.push(strategyObject);
		
    strategyObject = {};
    strategyObject[count <= 12] = this.lessThanTwelveItemsStrategy;
    productRemovalStrategies.push(strategyObject);

    strategyObject = {};
    strategyObject[$wishlistList.length] = this.wishListExistsStrategy;
    productRemovalStrategies.push(strategyObject);

    strategyObject = {};
    strategyObject[!$(wishlistData).find(".wishlist-list__body").length] = () => this.noWishlistBodyStrategy(wishlistData);
    productRemovalStrategies.push(strategyObject);
		
    this.execStrategies(productRemovalStrategies);
		
    this.defaultWishListBodyStrategy(count);
		
    return false;
  }
  static execStrategies(strategies) {
    strategies.forEach((item, index) => {
	if(Object.keys(item)[0] === 'true') {
	  item[Object.keys(item)[0]]();
	} 
    })
  }
  static getCount(wishlistData) {
    return parseInt(
      $(wishlistData)
        .find("[data-wishlist-item-count]")
        .attr("data-wishlist-item-count"),
      10
    );
  }
  static defaultWishListBodyStrategy(count) {
    $wishlistCount.html(count);
    $wishlistCount.attr("data-wishlist-item-count", count);

    this.refreshWishListRollover();
  }

  static noWishlistBodyStrategy(wishlistData) {
    const $listerContainer = $(".wishlist");
    $listerContainer.html($(wishlistData).find(".wishlist").html());
  }

  static emptyWishListStrategy() {
    $myFavouritesSendList.remove();

    if ($myFavouritesRolloverContainer.length) {
      $myFavouritesRolloverContainer.remove();
      $myFavouritesRolloverControls.remove();

      $myFavouritesRollover.prepend(emptyWishlistHTML);
    }
  }

  static wishListExistsStrategy(wishlistData) {
    startRefreshEffects($wishlistList);

    if ($(".wishlist--limit-achieved").length)
      $(".wishlist--limit-achieved").remove();
    $wishlistList.html($(wishlistData).find(".wishlist-list__body").html());
    window.BB.product.bindToAddToCartForm();
    if ($(".js-load-more-favourites").length) {
      $(".js-load-more-favourites").find("span").html(`(${count})`);
    } else {
      $(".column-block").show();
    }

    $(".remove-favourite").removeAttr("disabled").removeClass("disabled");

    initWishlistATB();
    setTimeout(() => endRefreshEffects($wishlistList), 500);
  }

  static lessThanTwelveItemsStrategy() {
    $(".js-load-more-favourites").hide();
    $(".column-block").show();
  }