Which units did you draw? If it wasn't the 19, 23-28 units, you will probably have a little harder time of it (last year's harvest data shows about 10% less success in the units not in the SW corner of the state). I tried and failed three times down by Carlsbad to find Javelina, and never laid eyes on one despite several people telling me they were there and seeing some sign of them.
As to your question about them congregating on private land, I don't personally think they would tend to do that. The one I harvested in 2010 was on public land, and all of the sign I found left by them was on public land (because that was the only land I could hunt), and I think if you put in enough leg work and use your optics heavily in the SW corner of the state - Silver City, Deming, Lordsburg area - you will probably find one.
From my somewhat limited experience, they aren't the hardest animals to stalk as their eyesight is very poor, and as long as you keep your wind good, you should be OK with a bow. I hunted with a rifle, and ended up shooting mine at about 20 yards, and I was wishing I had just taken my bow instead because the stalking part was pretty easy. I have also seen a couple of videos where people have used a predator call very successfully to call them in.
Overall, it is a very fun little hunt to help quell the end-of-season blues, and they make a unique mount to add to your collection. I wouldn't count on having any wonderful pork chops though. Javelina is the one hoofed, big game animal in NM that you do not have to eat (Page 24 of the BGRIB), and I am glad for it, because they are nasty. I tried very hard to enjoy it just because I try to consume all of what I kill, but despite my best efforts, I couldn't stomach it. It smells like skunk and tastes like skunk, and no one could convince me otherwise (the one I took was a mature boar, so that may have made it worse, but I think they are generally pretty gnarly eating).
Bottom line is look for lots of prickly pear that has the tops shredded, and look for tracks that look like doe/fawn tracks with a shorter stride, and glass the area heavily. Ultimately, just enjoy the fact that you are in the field pursuing something.
I would also recommend javelinahunter.com as it has quite a bit of useful information that was helpful for me. The video "Pure Hunting Javelina" is also useful, interesting to watch, and they use a predator call in a couple hunts on that video also.
Good luck. Post some pictures if you get one.
