Google "02E DSG self study guide" and you can find a .pdf of the VAG basic introduction for that transmission.
They do not service parts of the M-unit. This is pretty typical, lots of manufacturers do not service individual components of a larger assembly. Therefor, they do not bother to publish any information on that granular of a level. The aftermarket sometimes has solutions for common problems, but not always.
You can certainly take the M-unit out, and take it all apart, and visually check things (like all the little tiny thimble strainers they have for debris clogging a passage) but as far as solenoids go, that will be harder beyond simply checking for ON/OFF unless you have a way to measure current AND have a known-good one right next to you to compare.
Toyota won't sell you hybrid battery parts either, but plenty of people have taken them apart and figured out ways to fix things in them. Same thing. But in this case, most folks would just install a new M-unit. I would. And that is what I would do for my customers if this problem came into our shop, and I would stand behind the repair because I am 99% sure that would fix it. Sorry if I do not have a silver bullet, or a wooden bullet (since you are clearly looking for something cheap), but...
