I have some detailed information and some experiences to share which may help. I am currently using tubeless tires without tubes on 1936 wheels. I have also used tubeless tires without tubes on stock Task Force wheels. In both cases the wheels held air and my concerns that I would see leaks around the rivets were unfounded. I had more trouble finding valve stems that would seal properly. Snap-in valve stems need to be fairly snug to prevent leaks. Those old tubes didn't have the same type stems and the outside of the wheels was much more likely to rust. I have used both silicone RTV and bead sealer around valve stems to help seal them properly. Additional issues can come up when the bead of the wheel is excessively rusted and pitted. Tubeless tires rely on pressure between the tire and wheel to create a sealing surface. Now here's where stuff gets a little tricky.
Tube type tires rely on the tube expanding to press the tire beads against the wheel. The tire does not have to seal against the wheel and in fact has to allow some air to leak out while the tube expands so the tube can fully contact the tire. Tubeless tires are just the opposite. Tubeless tires have to seal against the wheel before inflation, at least enough so you can begin to build air pressure while inflating the tire. Tubeless tire wheels are different than tube tires and it's important to understand the difference.
This is a picture of a wheel for tubeless tire.
Notice the raised portion of the wheel inboard of the bead surface? This is what causes a tire to "POP" when it is first inflated after being mounted on the wheel. It is what the tire repairman must force the tire to "pop" over with a bead breaker when dismounting the tire. And it is what holds the tire bead against the wheel when the the tire is flat.
This is a tube type wheel:
Notice there is no raised area near the bead surface? This means there is nothing to seal the tire against the wheel when the tire is flat. And this can be a huge issue. For example, if your tire goes flat while the truck is parked, the tire literally falls inside the wheel leaving a massive gap between the tire and wheel. You're not just going to hook up a compressor and air that thing up. You have to find some way to get the tire to contact the wheel while delivering enough air to cause the tire to fully contact the wheel on both sides. If your tire is a bit narrow at the bead surface and does not naturally expand enough to contact the wheel? Same battle. Somehow you need to get the tire expanded and get enough air into the tire to make the tire contact the wheel so it will seal due to air pressure. And what if the pressure gets low while you're driving? It's possible that a turn or bump or sidewall hit is enough to temporarily break the seal and suddenly the tire is flat. That fast.
What can make this issue a bit more complicated is that bias-ply tires traditionally have stiff sidewalls while radials have more flexible sidewalls. This doesn't mean that one type tire works better in tubeless operation, but that it's important to match tire and wheel so they fit together as snugly as possible before inflation. How do you find this without a "try before you buy?" I'm not really sure.
Long story short is that you are better off using tubes in the tires when you're using tube type wheels if you can afford it. Radial tubes for radial tires due to the additional flexibility and movement of the tire. My experience is that bias-ply tires work with either tube type but folks in the know recommend bias tubes for bias tires.
Good luck.