I'm gonna be honest the Gold Shovel was not even worth it. Because I've been using like normal shovels that can be customized so that way it restarts the durability I have used the gold shovel less. You wanna know the worst part? The Gold Shovel cannot be customized and the same goes for any other golden tool.
I finally bothered to check my catalog to see how many Gulliver items I've actually obtained, and the answer seems to be twenty-four. So, in theory, I need to help him six more times to get the gold shovel recipe. Which will most likely take a lot more than six weeks, given how rarely he seems to show up. But now I feel less irritated, knowing that I really haven't seen him that many times yet. The game isn't necesarily messing up, it's just taking a ridiculous amount of time.