I ended up reading all the documentation provided alongside the auction because I was debating making a bid. I decided not to in the end.
In total, Cheyenne weighs in around ~95000lbs in weight, they require it be broken down in <= 3 business days on site and only offer 8AM - 4PM access. Therefore you'll need to support unbolting and palletizing all the cabinets for loading into a dry trailer, get a truck to show up, load, then FTL to the storage (or reinstall) location of your choosing for whatever's next.
Requirements for getting facility access seem to mean you bring both labor and any/all specialized equipment including protective equipment to not damage their floors while hauling away those 2400lb racks. Liability insurance of $1-2M across a wide range of categories (this isn't particularly unusual, or expensive, but it does mean you can't just show up with some mates and a truck you rented at Home Depot).
I'd guess you're looking at more like $25k just to move Cheyenne via truck, plus whatever it sells for at auction, unless you are located almost next door to them in Wyoming. Going from WY to WA the FTL costs alone would be $6-7k USD just for the freight cost (driver, dry trailer and fuel surcharges), add a bit if your destination doesn't have a loading dock and needs transloading for the last mile to >1 truck (probably) equipped with a tail lift. All the rest is finding a local contractor with semi-skilled labor and equipment to break it down and get it ready to load on a truck and covering the "job insurance".
Warehouse costs if you're breaking it for parts won't be trivial either and you'd be flooding the used market (unfavorably to you) were you to list 8000 CPUs or 300TB DDR4; it could take months or even to clear the parts without selling at a substantially depressed price.
It will take probably several thousand hours in labor to break this for parts assuming you need to sell them "Tested and Working" to achieve the $50/CPU unit pricing another commenter noticed on eBay, and "Untested; Sold as Seen" won't get anywhere near the same $/unit (for CPUs, DRAM, or anything else) and so even assuming $25/hr for fully burdened relatively unskilled labor, you could well be talking up to $100k in labor to break, test and list Cheyenne's guts on eBay or even sell onward in lots to other recyclers / used parts resellers. I don't think I could even find $25/hr labor in WA capable and willing of undertaking this work, I fear it'd be more like $45-60/hr in this market in 2024 (and this alone makes the idea of bidding unviable).
A lot of the components like the Cooling Distribution Units are, in my opinion, worth little more than scrap metal unless you're really going to try and make Cheyenne live again (which makes no sense, it's a 1.7MW supercomputer costing thousands of dollars per day to power, and which has similar TFLOPs to something needing 100x less power if you'd bought 2024-era hardware instead).
Anything you ultimately can't sell as parts or shift as scrap metal you are potentially going to have to junk (at cost) or send to specialist electronics recycling (at cost); your obligations here are going to vary by location and this could also be expensive -- the leftovers.
If anyone does take the plunge, please do write up your experiences!
For example, in April ebay sold 79 of them. You're looking at ~100 months. And that's assuming constant demand.