My cat insists on being pet. He will insistently meow until someone comes to him and pets him. After just a few seconds, he will take a few steps away and look back, asking for more pets. He leads me on completely random paths throughout my house on these little petting excursions.
He is not leading me to anywhere specific. No matter how long I continue this behavior, he never leads me anywhere consistent. He just keeps going in completely random directions until I stop, and have continued this for over an hour before.
He is very well loved by both his older cat sibling and my fiance and I, I wake up with him cuddling me in the morning most times and pet him for a long while. Not sure if relevant but he also HATES being picked up.
He never wants for food and I replace his water every day. He has two high quality litter boxes and we recently moved to a new house. We had to stay in a hotel for about a week and at no point before, during or after the move did this walking around while being pet behavior change in any way. He is a little over a year old and has been doing this since January-ish I would guess.