Yes, I wish Moho's lighting tools controls were more accessible and
interactive. Sometimes I have to nest a bunch of FX within the character to get a certain look but it's a pain when I need to change the lighting direction or color, or animate all the Light FX together. I guess maybe I could tie some controls to Smart Bones that's really too much trouble to do for every character.
My feeling is that Moho's lighting tools work well with simpler characters and animation, but you quickly to run into problems with more complicated character designs and animations.
What I've been doing lately is setting up Layer Comps for each character to make it easier to light in After Effects. For example, splitting the arms from the body so I have masking elements that allow me to light the arms across the body, or to withhold lighting from parts that should be occluded in 'shadow'. This needs to be set up on a scene by scene basis but it's pretty easy to do, and a whole lot easier to work with once you have it set up. Technically, you can replicate this in Moho but it's a lot easier in AE because you can see the effects live while adjusting them. (In other words: no endless Ctrl-R tests, it's all WYSIWYG.)
There are a number of tools available to AE for getting different lighting looks. There are Styles like the ones found in Photoshop, which you can tie to a global setting, and there are native and third-party fx plugins you can use for simulating light wraps, direction lighting, etc.
Most of the time, I'll just duplicate body part layers in AE, apply Set Channels to make the layers solid black or white, and then construct lighting masks from them by combining, blurring, and offsetting them. Then I can use that element to shade the characters. This gives me the most control over the look and animation of the shading effect, without using plugins and using only the direct output from Moho.
Sometimes I'll be asked to create a lighting effect that looks more organic, and the 'cheap' masking tricks in comp aren't cutting it. In this case, I might draw the lighting as shapes in Moho and use a reference of the whole character as a mask to cut out the light and shadow shapes. (I could do this in AE but in Moho I have the option to use bones to deform the lighting elements with the character.) This can look really cool but I try to reserve the approach for special cases because it takes more effort to set up and animate.
Anyway, there's are many ways to light Moho animations besides using just Moho. Just tossing out a few ideas.
(BTW, I only mentioned AE in the above examples but I've used Fusion with Moho layers the same way. The set up process is different but the ideas are the same.)