Edit: They have a link to their known locations.
When you see a photo of them, you almost always see the right side of the locomotive, as that's where the pistons and the drive train are. You almost never see the left side of it. The left side is much more uninteresting.
However, having seen them and been somewhat fascinated in them for years and years, when I finally saw one live, it never occurred to me that the cylinders were only on the right side. I simply projected that the other side has a similar set, just like every other locomotive.
Not only that, but the boilers tend to be a bit off center on the chassis also.
Just funny when all you have is one perspective, how someone can incorrectly fill in the rest from other knowledge that seems coherent, but it completely wrong.
"The most significant design difference between Shays and Heislers was the arrangement of the driving cylinders. The Shays had either two or three driving cylinders mounted on the right hand side of the locomotive. Since the weight of the driving cylinders sat only on one side, the boiler was mounted offset to the left to provide a counterbalance. In the Heislers, the driving cylinders were located in the middle of the locomotive."[1][2]
[1] https://www.friendsofno9.org/post/mechanic-s-corner-geared-l...
As Wikipedia partly mentions, Shay designs were very well suited to low-speed operation on dirt-cheap (often temporary) tracks. That generally meant narrow-gauge, light rail & iffy roadbed, tight curves, and steep grades. Low-speed-only was the only sort of operation you'd want to attempt - tracks suitable for higher speeds would have cost far more, but provided minimal benefit for logging, mining, and other Shay use cases.
A bit fuzzier, but I also recall Shays being considerably more easily maintained (vs. conventional steam locomotives) in situations with minimal facilities, equipment, and trained staff. Not sure how much that was locomotives being designed to the customers' needs, vs. being intrinsic to the Shay mechanical layout.
And a bit of context - a century or so ago, modern heavy road construction equipment and heavy trucks mostly didn't exist. Vs. railroad tech did. So for logging, mining, and many situations where we'd say "d'oh, just build a road and use trucks" - they just laid some RR track and used that.
Another very important difference (and one that makes Heislers superior to Shays) is that the driveshaft is centered on the loco frame.
That means the driveshaft doesn't need expansion joints, which tended to get jammed under high torque and prevent the trucks from pivoting under the local (thus splitting the rails).
[1] https://roaringcamp.com/excursions/redwood-forest-steam-trai...
Rails for high speed with safety, ride comfort and advanced signalling to maintain a scheduled service is a very different proposition to some temporary rails to get to the front line of a war, a new coal seam or forest 'port'. The latter is much easier compared to a road but now we have big machines for the latter, not the former.
Back in the day, I suspect they'd have covered much of that with tin* or wood, to cut down on cleaning, maintenance, & wear.
*Meaning "cheap, thin sheet metal"