I'm a bit fanatical about clean (if not dressed/"detailed") engine compartments, so whenever I buy something used it's a big part of my initial clean-up.
Heh heh, ten minutes? I know I'm one *very* slow detailer, but I've spent much longer than that on a single bracket! Knocking oxidation off underhood items (e.g., fuzzy-white-oxidized alternator housings) with a Dremel can take ages, especially when you can only see one side/angle from a given position. OTOH a decently clean one can go very fast so I guess it's just another one of those "it depends" things.
My experiences have shown that, as
WCD suggested, most modern engine compartments are pretty well sealed against water. There are some specific items (e.g., OptiSpark distributors in GMs) that need to stay dry, but I've gotten a *lot* of engine compartments very wet over the years and even the Jags

came through it OK.
If in doubt, cover it with plastic wrap, cover *that* with aluminum foil, and then clean the item in question later with great care.
I wouldn't leave them running, as a thorough job can take a while and I wouldn't want fans switching on/off or other electrical things happening while I'm working in there (imagine your holding that fan's blades to clean them when it switches on...).
Steamers are great but they don't always get down into inaccessible areas. For those I use long objects with swabs/foam/cloth/etc. somehow attached. The long "grabber" tools used for picking up/holding stuff (mine have three wire jaws and operate with a plunger) can be *very* helpful.
Dedicated citrus-based engine cleaners (Griot's works but is expensive, TOL/Hi-Temp stuff works and is cheap) are great and generally a lot milder than I would've expected. For things that aren't too nasty I like P21S TAW but some here tease me about that being so expensive and I bet something like a cheap APC would work fine too.
Consider where the nasty stuff is gonna go...floor drains? I have a commercial oil separator plumbed into my home shop, otherwise I'd be concerned about where all that stuff ends up environmental/health-wise.
For things you don't want to get wet (or that are really greasy, so much so that you don't want that [stuff] going anywhere else in the compartment as it gets cleaned off) I like solvents like AutoInt's New Car Prep.
You oughta be able to get the Tacoma pretty nice, I did OK on my Blazer and it was a filthy mess when I started. And FWIW it still looks OK after this last winter, but then I do a cursory cleaning every time I wash it.