Did that last year on Route 14. Gas is available in Ranchester after you get off of the Interstate, just before entering the Bighorns. Also in Shell, Wyo. after leaving on the west side. I'm pretty sure we did it on one fill from Devil's Tower to Cody (10 mpg, 34 gal. tank), as I don't see any charges on my credit card for that area. Can do it in one day, but we camped there for 2 nights.
Be prepared for long uphill pulls (6% grade) going up, with many 20 mph turns, maybe even as slow as 15 mph. Very doable, just slow. Extremely scenic.
Downhill on the other side is a long descent, almost 22 miles at 6% - despite primarily engine braking, I got my brakes very hot. Ditto on having very slow, windy curves going down. Again no issues, just take it slow. There are a fair number of good pullouts for vista viewing/cooling off if needed.
We love the Bighorns. Campgrounds are small, and seemed to be pretty full most of the time (early June), but as it is BLM land, there are huge opportunities for off road camping (boondocking). Many "villages" of boondockers seen when we explored off the main road. Campground spots are reservable and cheap (limited availability of hookups, though). Boondocking is, of course, free.
Haven't driven it, but all advice is to avoid 14A.
Can't advise on 16 - did it too many years ago to remember pluses/minuses.
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