Because Canon doesn't license its mount or give the internal details of the electronic communication to third parties, nearly everyone has to reverse engineer the mount communication signals. So this is the main danger of going with a 3rd party lens (particularly an old one)--that when the lens is new, it will communicate properly, but that with older cameras or future ones, that compatibility could be compromised.
When Canon updated their camera mount to support EF-S digital lenses/bodies, a lot of film-era 3rd-party lenses--most particularly in autofocus function--were compromised. Makers like Sigma, Tokina, and Tamron would often offer to rechip the lens to bring back function, but only for a limited period of time. It's unlikely that Tokina will rechip your lens at this late date (and the fact that AF works on the 6D indicates that it may have already been rechipped).
The incompatibility you ran into is likely why someone felt they wanted to sell it, and could be why you got a bargain price. It's also why saving up the pennies for an EF 400/5.6L might be worth it in the long run.
It is odd that the lens works on a full frame but not a crop body. I would suggest looking closely at the physical coupling for the mount against that of an EF-S lens, and seeing if there's something on the mount that blocks/prevents it from mounting fully/properly on a crop body, and keeping the chip contacts from mating properly with the pins on the camera body (the behavior you describe is what happens when the camera can't sense any lens at all on the mount). And then, depending on how daring you are, consider getting out a dremel tool :D, returning the lens and saving up pennies for a Canon 400/5.6, or just getting used to cropping 6D shots with it.