With that lens causing 01 Err, which indicates a fault in the lens-to-camera communication, there are three main possibilities...
#1. Communication is interrupted by faulty lens-to-camera contacts. Cleaning the contacts, as you have already done, usually solves this. Do this with a few drops isopropyl alcohol on a clean, lint-free cloth.
Note: DO NOT use Q-tips, as the common household type of "cotton buds" tend to shed tiny threads that can get into and jam a camera's mechanisms. There are "optical" quality swabs that are safe to use, but cost much more than the usual household type. Some suggest, but I also don't recommend using a pencil eraser because the usual cause of problems is oils (finger oils, oil from camera mechanisms) on the contacts, and pencil erasers are made from vegetable oil. Also DO NOT use anything abrasive. The contacts are usually gold plated to prevent oxidization, but that plating is more easily damaged.
Also check the "pins" just inside the front of the camera, that correspond to the contacts on the rear of the lens. Those pins may need cleaning, too. And they are spring loaded to insure a good connection. Gently press each one to see if any of them appear "sticky".
#2. An actual fault within the lens is another possibility. A sticky aperture, failed motor for the AF or aperture driving mechanism, loose or broken wiring all are possibilities. These are well beyond most peoples' DIY repair capabilities, but there is at least thing you can check... The AF off/on switch. Operate it a few times. Most of the time those switches are self-cleaning. They can get oxidized inside just sitting, but operating them a few times often clears up any issues.
Most Tokina lenses I've seen have an unusual AF off/on switch, where you slide the focus ring forward or backward to enable, disable AF. But it should be similar, that you can get it to "self clean" the switch mechanism just by operating it.
Macro lenses in particular also sometimes have focus limiter switches. If so, I'd recommend operating that too... and make sure it's set to the correct range where you are trying to focus. Having one set in the wrong range will make focus problems.
#3. Finally, it's possible that an older third party lens is simply incompatible with a later camera model. Third party lens manufacturers do not license the technology from the camera manufacturer. They instead reverse engineer it. Because of this, if the camera manufacturer later changes how their cameras "talk to" the lens in some way, there is no guarantee of backward compatibility with a third party lens.
This was a common problem with Sigma lenses and Canon cameras a few years ago. There have been some issues with a few Tamron lenses and Canon cameras, too. Tokina has not had many problems I'm aware of and I couldn't find anything posted online about that specific lens on a 5DII in particular. Usually when there's an issue, someone posts about it somewhere online.
If there is a compatibility issue between Tokina 100mm macro lens of certain age and 5D Mark II, just trying the lens on another Canon might not tell you much. It may work on earlier... sometimes but more rarely even on later models... but just not "play well" with anything later or one or a few particular cameras.
For example, I have an old Sigma 24-75mm lens that works find on older Canon EOS-3 film and 10D digital cameras... but "locks up" any later Canon cameras with an Err 01, as soon as the camera attempts to autofocus the lens.
Possible future incompatibility issues is one of the risks of buying third party lenses and partly why they are often less expensive than OEM lenses.
The camera manufacturers are pretty good about making their own lenses fully compatible with old, current and future camera models... especially Canon. There are virtually no compatibility issues between any of the 100 million Canon EF lenses made to date and any of the EOS camera models offered over the past 25 years. An exception is the EF-S lenses, designed specifically for "crop sensor" cameras and not usable on old film cameras or any of the full frame or APS-H digital models.
Nikon doesn't do as well with this. They have tried to maintain at least a modicum of compatibility all the way back to the beginning of their SLR system around 1960, while Canon made a clean break going from the FL/FD mount to the EF/EOS mount in the late 1980s (that pissed a lot of Canon users off at the time). But Nikon's approach has resulted in a lot more compatibility issue "footnotes", both over the years and currently. There are extensive charts showing which Nikon lenses work on which Nikon cameras, and whether they are fully or only partially compatible... Not to mention third party lenses made to fit Nikon. In Nikon F mount there are non-AI, AI, AI-S, AF, AF-D and AF-S lenses... some of which work with some cameras but not with others, or only in some limited ways with others. Check out:
http://www.nikonians.org/reviews?alias=nikon-slr-camera-and-lens-compatibility and
http://www.kenrockwell.com/nikon/compatibility-lens.htmYou might want to consult those and other charts before purchasing more lenses.
Frankly, I don't envy you trying to switch back and forth using Canon and Nikon systems alongside each other.... having to learn the nuances of both. That's sort of like using a Mac and a PC on alternating days. But, back to your original problem with the 100mm Tokina on the 5DII:
It sounds as if you have pretty well ruled out #1... dirty/oily contacts (though you should check the pins on the camera, too). And, I don't find any evidence of #3... known incompatibility issues with that particular lens and camera.
So that leaves #2... some sort of mechanical or electronic failure of the lens itself. Try operating the AF on/off and/or focus limiter switches back an forth a number of times to see if that helps in any way. If so, great! If not, unless you are willing to spend money having the lens checked by a repair tech and have it fixed if needed, you're probably wise to try to return it to the seller. Don't let it sour you on Tokina lenses or Canon cameras though. Both can be very good (in fact, more than a few Nikon lenses are made for them by Tokina, it appears).
I don't think this problem necessarily reflects on the seller in the auction either (I've done thousands of auction transactions as both buyer and seller, and find the vast majority of people are quite honest). They may have bought the lens locally and simply have no means of testing it.... Or it might work fine on an older/different camera model they have. Hard to say. I always try to assume the best of people, until I see evidence otherwise. Anyway, I hope they will work with you either to return the lens for a refund or to refund you the cost of having it repaired.