There are a lot of signs to look for, mainly because there are seven senses that can be stimulated. There are the five you usually think of and there's also vestibular (balance and spatial orientation) and proprioceptive (the relative position of neighboring parts of the body). Some stereotypically autistic behaviors (known as stims) are signs; hitting or banging one's head, spinning self or objects, hand flapping, jumping up and down, etc. Some kids who are sensory seeking are on the spectrum and some aren't, so these behaviors don't necessarily mean that the child is on the spectrum.
Also, just because the child is sensory-seeking in one area doesn't mean that he'll be sensory-seeking in all areas. People can be both sensory seekers and sensory avoiders. It also changes with the amount of sensory input a person gets. One kid might love to spin when he controls how fast he goes and how long he spins for, but put him on a spinning amusement park ride and he won't want anything to do with it. It might even make him sick.
Kids who are sensory seekers tend to be the kids who are loud, energetic, and rowdy. Most like jumping off of furniture and crashing onto other furniture. They're typically the kids who are extroverted, always on the go, love to roughhouse, stuff like that. I don't know if I can give you The Signs that This Child is a Sensory Seeker, KWIM? Like most matters of the brain, it isn't as cut and dried as most people would like it to be. All sensory seeking kids are different from each other and not many children are textbook cases. HTH.