Very cool!
I'm wondering how our cat would take to a harness. She's pretty laid back, so maybe?
Plus, cat and dog in a car. With my dog, that could end up in a war.
It's all about baby steps. I put a light harness on my cat to wear around the house when he was much younger. He got used to wearing it. Initially he would lay down from the extra weight, but it wasn't long before he got used to the feeling and would carry on about his normal business.
I think it also helped that he is very comfortable walking very close to my feet. I never made him feel like he should get out of my way because I like that he wanted to be close to me. Some cats don't like you standing over them too close if they've had trauma associated with being stepped on. A cat that doesn't feel comfortable standing very close to you will be very difficult to leash train because they will have a tendency to be far away from you.
Using the leash indoors or in their own safe environment is a must, at least in the beginning. I learned the hard way that taking them outside on the lead for the first time is a bad idea. It took my cat a month to get used to being tethered to me. He pulled and jerked and tried to run away. I just took it easy and let him lead the walk. In the beginning you can't pull the leash at all and hope to get any cooperation. It took quite a while before my cat figured out the nuance of the gentle leash pull. If he doesn't cooperate I stand between him and the direction he wants to go, or I give him a light pat on the back of his tail and he gets the idea. That takes a lot of work, but he's made great progress over the years. Again, the key in my cats case is that I let him lead the walk 80% of the time. I'm just there to keep him out of danger.
One thing I noticed is that he likes to walk the length of walls, fences, etc. I think this may be common for cats, I'm not sure. 99% of the time I can count on him walking the entire length of a wall. So planning walks this way lends to a good amount of predictability.
The biggest challenge is the environment outdoors. Loud noises, cars, dogs, etc. can turn a pleasant walk into a frantic nightmare of nerves. This is typically the biggest hurdle. My cat is pretty chill, but he is a cat and can be spooked far easier than a dog can. I'm always on the lookout and I've gotten pretty good at mitigating these type of events.
It's a work in progress and I'm still learning new techniques when I walk him. I also treat our walks as meditation because every animal lives fully in the moment, so I try to follow his example and live more of my life in the now like he does. So when I walk with him, I observe and try to focus on the immediate surroundings, the sounds my footsteps make, the wind, surrounding noises, etc. That way I can experience a walking meditation and also be more aware of any impending danger which may be headed his way. I've had a few close calls, but was able to shield him from any frantic events simply because I was paying close attention to my surroundings instead of being on my phone, or thinking about something else.