If I were to buy a "mainstream" gas powered dumptruck, it would be 8.1L powered or possibly a Ford 429 "Lima" gasser. The older IH 345's & 392's are just too old usually to find in good running condition.
The 8.1L is a tough 500 cu in. gas motor with a lot of torque down low and enough rotating mass to get the job done. Gotta watch for the weakness of the 8.1 and that's a soft knock sound. I think it's a spark knock and it upsets some pickup owners, they think the engine is defective, but it's not.
I am starting a business and I am guessing that I will be putting less than 12k miles on it per year.
Then a gas motor is on the borderline. I don't know how many miles are on it now, but 12K/yr is about max for a gasser in a truck that size to expect a 10 yr lifespan between rebuilds. Nice thing is a reman 8.1L is probably cheap. GM is basically the last company to build a truck of that size with available big block gas power.
If that truck is 26,000lbs, I'd estimate an empty weight of ~12,000lbs. With that power plant it will easily trailer up to 20,000lbs or haul 7 tons in the bed.
The area where I live is very hilly.
That would only be a problem when fully loaded. You will not enjoy the low end torque benefits of a diesel when climbing a hill from a dead stop and will consume quite a bit more fuel. However, if I were to pick a gas motor to use, it would be the 8.1L since it develops respectable torque down low.
It's no Peterbilt or IH , but it's a perfect "starter" dumptruck and hopefully it's cheap. I agree with the other guys that diesel is a better choice, but I've been in your shoes-I had to buy 2 gas dumptrucks (an IH S-1600 & IH S-1700, 345 & 392 gas respectively) before I could pay for a diesel dumptruck. My first was a '89 F-700 with a 6.6L diesel. A whopping 180HP.
Double frames are nice, but not a necessity unless you're off road and dumping heavy loads many times. A single frame dump is fine if you're reasonably careful with it. 7 ton loads are not a big problem on a strong single frame.
I can't tell if it has airbrakes. I really like airbrakes, but newer hydraulic disc brakes are way better than the old hyraulic drums I had to fix myself.
The thing I don't like is the price. That's too expensive for the times we live in right now. I would think you could find a similar gas dumptruck down close to 20K. For $27,000, I know you could get a clean airbraked diesel dumptruck.