I used rubber gloves the first few times I tung oiled my 7620's nec, but lately I just stopped bothering- it's not too hard to get off your hands when it's done.
You don't want to apply tung oil over your neck's finish- you want to sand it down to bare wood and then apply the tung oil, as it's supposed to be a penetrating finish. Then you sand it back down again until it's essentially down to bare wood, just bare wood with the pores protected by tung oil. At least, this is my understanding, that you're not trying to build up a coat... correct?
Also, in my experience you're probably going to want a new coat every 6 months or so.
I LOVE the feel of a tung oiled neck, but especially with a 7-string in new england's notoriously shifty climate, you have to accept thefact that, as the wood is no logner 100% sealed, you will be doing at least one new setup a season, if not more- there are definite shifts corresponding to humidity changes, as the (essentially) bare wood is much more responsive to climate changes. I think my next 7, I'll just leave the finish on- it's a little tackier, but hopefully will be more stable.