At time when Im searching for my gig its nowhere to be found. Sometimes its on the first page. Do they rotate every now and then?

There really doesn't seem to be anything that they constantly use to rank sites in the search results of fiverr. I think they randomly show them sometimes. You can edit a gig sometimes and have it show up higher in the search results sometimes but it don't work all the time

Add a video, put unique picture, place relevant keywords - tags, advertise it. Also make it express with catchy - clear title. Your gig should be shown in the searches, the first orders are the hardest, that's why you'll need to advertise it