NOTE: This advice refers to finishing smaller projects with relatively small surface area, like bokkens (wooden training weapons). Tung oil is one of the best choices for these, however, that's not always the case in other applications, like large furniture (unless you know what you're doing).
From my experience with pure tung oil, if you treat it like every other finish and just let it sit, it will never cure. No, literally never. The only way for pure tung oil to cure in a realistic time-frame is to optimize your curing environment.
Factors that determine the curing speed are humidity, temperature, coat thickness, and most importantly, number of air changes per hour. If the temperature is below 50 degrees, don't bother. 70 is acceptable, 90+ is best. Humidity in the curing environment shouldn't exceed 30%, the less the better. Higher humidity means more water and less oxygen in the same amount of air—and likewise—drier air means more oxygen can form long chains with the oil, which is how tung oil cures.
Let's cover the number of air changes per hour. Simply put, it's the number of times all the air in the interior gets replaced with new air (within an hour). The more fresh air enters and mixes with the curing air, the more oxygen is delivered to the oil.
It is the most crucial factor, since even if your humidity is at 5%, but there is no air-flow coming in, the oil will just sit there and wait for you to remedy the problem, while you're waiting for it to cure.
The last factor but no less important is your coat thickness. With tung oil it's simple—more thin coats is much better than less thicker coats. In a thick coat, oxygen can't reach all of the oil, and the surface will forever feel rubbery and very sticky. Be sure to wipe off the excess oil no more than 10 minutes after applying the coat. Some people wait 30min, some as long as an hour. It's a big mistake that leaves the oil beneath the surface unable to cure (as with thick coats), and renders your finish ruined.
First time I was using pure tung oil, I had an open window, but no forced air-flow. I also applied too thick coats of oil, and waited too long before wiping off the excess. I waited 6 weeks for one coat to cure, and it never did. Next time, in addition to applying thin coats well rubbed into the wood, I put a cheap 9" fan in that same window, blowing fresh air directly onto my project, and each of my tung oil coats cured within 4-5 days, which for pure tung oil truly is the speed of light. Thanks to the forced flow of fresh air, my number of air changes per hour increased dramatically, as opposed to no air-flow. For the same reason, the smaller the interior you're curing tung oil in, the less air needs to be replaced, and the faster the curing.
As for "how long till I can re-coat?", pure tung oil requires that each coat be completely cured before you can re-apply the oil. There are no shortcuts and no "minimal curing time". How to tell if it's cured?
There are a few behaviors the finish has to display.
First, the finish cannot feel sticky to the hand, at all, whatsoever. If it does, the oil isn't done reacting with oxygen. You can perform a "tissue test", where you firmly press a tissue against the finish with your finger, then slowly pull it away. If any tissue fibers get caught in the oil, you know it's nowhere near being cured. Also, there can be no oil odor on your hand after touching the finish, and no odor on the cloth after briskly rubbing the finish. All those behaviors will occur in this order as the oil continues to cure. Ultimately, only when there is NO detectable oil odor once you smell the finish up close and there's absolutely no sticky feel to the surface, the finish is ready for another coat. When oiling bokkens, I leave it for another 24-48h after there's no detectable smell.
Experiment, examine your results and see what can be improved in your tung oil application process next time around. And remember not to give up! Dealing with tung oil is like taking care of a 2-weeks-old kitten, but it's the best wood finish (for wooden weapons) and well worth it.