First:
When thinking about mounting location, remember that someone else will be filling this tank. They need easy and safe access. If they have to crawl under the trailer, lay on the ground, or position themselves in front of the purge valve, you may not be able to get it filled. Easy, safe access.
They will also need some place, likely on the tank itself, to clamp a ground cable.
Secondly:
I have had several ASME tanks.
I don't want another one, unless it's attached to a vehicle that I absolutely want for everything else about it.
Unless you know that you will always be able to fill the tank at a good propane supplier that knows what they're doing, I recommend sticking with DOT tanks. They're easier to work with, easier to fill, and easier to get inspected (most places).
My biggest problems with ASME tanks come back to the whole "certified for life" thing. They don't need to be inspected, which means they don't get inspected, which means few people know how to inspect them. And if you do find a place that will do ASME inspections, they almost never restamp them. ...But if they do, it's only if the tank is empty and purged. (Which takes time and costs much more than for DOT tanks.)
And that lack of an updated inspection stamp means that at least 95% of places where you might stop for propane will see the "expired" certification stamp and refuse to fill the tank, only fill it after giving you a hard time and needing you to show them that ASME tanks don't get recertified, hem and haw for 10 minutes before "doing it for you just this once", or claim that they don't know how.
I have even seen
many predatory/shady RV centers claim that an ASME tank was "expired" and had to be recertified, for a not-insignificant fee, before they would fill the tank. (Even my grandfather fell for this, with a $75 fee, once; and a $150 fee the second time. They put a generic 'hologram' type sticker on the tank that said "Certified and Inspected" and wrote the date with a paint pen.
)
The theory of a permanently mounted tank that can be tucked out of the way and never needs to be inspected is appealing.
And it can work well if you have a good propane supplier that knows ASME tanks, and you'll only be using that supplier and staying close to 'home base' the majority of the time.
But, when out on the road - especially for long trips - ASME tanks are nothing but a headache and feel like a liability.
It's like having an electric car, and having to plan trips based on where charging stations are located; or going back to the '80s and having to plan a trip based on where you could get diesel fuel.