Thetford (spelling)? has a product recommended for cleaning the toilet. Start with that and use it until you become more familiar with your unit, and figure out what to use for different applications. You should be able to find it at any RV dealer, or Walmart usually has it.
Naw Scott, don't worry 'bout it, they're self cleaning, no?
BTW, I have heard of some that keep one of those soaker things handy to help wash out the larger chunks ....
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Ruck -n- Ella