The 1st time I put a harness on Shango, it was nearly impossible. He wanted nothing to do with it. Once I finally got it on him, he would then flop over like the weight of it was just too much to bear. Then he'd start doing somersaults trying to get out of it. I ignored his dislike and got out a wand toy. He completely forgot about the harness because he was too focused on playing. After about an hour, I took the harness off. After doing that for about 1-2 weeks, I then put the harness on him and then with the harness on put him in his cat stroller and took him for walks around the property. He then started to associate the harness as being a positive experience because he got to go outside and that is when it got much easier to put the harness on him.
I always took him on the same walks making loops all the way around our property to familiarize him with the area. After a couple of weeks in the stroller only, I'd do 1-2 laps around the property and then once I got back to the backyard would take him out of his stroller (the stroller has a leash tether I would clip onto the harness, I always clip the leash onto the harness before un-clipping him from the stroller...just in case). I never tried to force him to walk, I just simply set him down next to his stroller. After taking a few minutes to just look around, he started to wander around exploring the outside world. The 1st time he didn't wander around too much and mainly stayed in the backyard. Then the next day, he started to walk around the property just like we'd do when he was in the stroller. He then started to love his harness. All I had to do was take it out and he'd come running over to me so I could put it on him. After about a month he started to feel confident enough to roam further away where I never took him before in the stroller. He even learned very quickly where the gates were at to the fences so once we'd make a loop around the back property, he'd go right to the gate to then go somewhere else.
Shango loves going for walks around our house, but hates completely unfamiliar places. I take him with me on business trips and thought he'd enjoy taking a walk with me in TX... boy was I wrong. After about 5 minutes I took him back inside. The next time I took the harness out, instead of running to me wanting me to put it on him, he hissed at it and ran away. I decided to try 1 more time in the stroller and took him to a walking trail. He ended up loving the experience as long as he was in his stroller. I learned very quickly that he prefers the harness in CO where he's more familiar with his surroundings and anywhere else he wants to be in his stroller.
Keep in mind that not all cats will like walking on a harness. I wouldn't try to force him to walk if he's not enjoying the experience. You might want to try a cat stroller or maybe just sit down on the grass with him and let him look around. Then he might start feeling more confident and start to walk around on his own. Savannah's are very curious and usually won't want to stay sitting in one place for too long when there's so many other things to explore.