Ok, easy enough to play with intent as I understand it from that frame of reference.
This is just a basic exercise that allows you to GET a physical sense of how you can play with intent for some "navel gazing" fun, and not necessarily for application of fighting, although, the method itself will put power into your Karate if you get creative with the idea in your overall continued practice of the method.
You have just snapped into soto uke and are at the terminus of the blocking action (as though you just blocked) as you would in kata. Hold that posture and relax everything while remaining in that stance. Start with your hands relaxing while forming fists but it's like you have a round wooden dowel in each of your hands, about the size of your index finger.
Let your elbows feel like they're sinking toward the floor like they have weights hanging from them, but don't actually lower them with any kind of effort or let their positioning alter your overall stance. Relax your shoulders so your scapulae drop toward your hips. You're holding soto uke but in a relaxed, soft manner.
Focus on your fingertips touching your palms. If you're right side forward, focus on the fingertips of your right hand as they rest against your palm. With all the intent you can apply to opening your right hand, don't. Hold your fingers in their softened state while you focus every bit of your intent to open your hand while keeping it closed. Focus on your fingertips softly touching your palm and check yourself for any tension throughout your body and release it before it's allowed to build.
Try it for a few minutes and switch sides.
Now for some really fun "navel gazing"
Stand in soto uke in the same relaxed manner as you did while working on your hands. Imagine a cable attached to your forward elbow and forward knee. With all the force of intent you played with earlier, lift your forward knee with your forward elbow. You don't need the arresting/opposing hold against the intent of lifting the knee because it's pretty much impossible to physically do that. The same 'resistance' you felt while working the hands is what you're trying to dial in with lifting your knees.
You can do a simpler exercise while sitting on a kitchen chair.
Place your hands on your thighs while seated, and relax your entire body while sitting up straight. Let your elbows and shoulders 'drop' as you did in soto uke ,while holding your elbows slightly forward. Now stand up with the full force of your intent to do so.
There will inevitably be tension as you work through the exercises and it's important to let it happen a little bit so you can modulate it and allow it to show itself so as to understand how it networks in your body because it's different for everyone. The modulation and conscious directing of tension into the 'channels' through which it travels is at least as important to explore and understand as the idea of being relaxed.
It isn't all there is to it, but it's a glimpse into the kinds of work I'm familiar with in exploring the solo work of applied intent.
Look forward to reading your feedback if you're willing to share it here.