Yes, definitely don't reuse original rubber, or stuff even more than a year or so old. Even if it holds together in removal (doubtful), it won't seal well on reinstallation. You can reuse the chrome trim, though, and should if it's in good condition. From the FSM:
removal and installation of the tailgate glass is same as for windshield glass with exception that a sealing agent is used rather than an adhesive.
I would note that although it's flatness does make the rear glass easy to deal with, it is a lot heavier than you would expect, so be ready for some precision heavy lifting, particularly if you like your paint and don't want to chip the glass edge (which leaves it vulnerable to cracking later).
Anyway, *carefully* remove the chrome trim (a really wide blade, thin putty knife or scraper is good for this) around the outside of the window. You can use a screwdriver, just be careful not to destroy the trim, it's expensive for what it is. Then, from the outside, loosen the rubber from the flange, using your putty knife/scraper/spatula/screwdriver. Push the weather stripping to the outside (away from the glass edge), preferably at the top, kind of near the corner, and tap at the glass to remove it to the outside. I like using a heavy pair of mechanic's gloves and using the heel of my hand for that last part. It's not as hard as tools, so you don't worry about breaking the glass. It is fairly durable, but also really expensive (defroster lines...) so why risk breaking it? And the glove protects me reasonably (along with coverall long sleeves) if the glass does break, or if the edges are sharp. Once you get the glass started out of the weatherstrip, work your way around 'til enough is loose that it can come out. An extra pair of hands is nice for that part, and hopefully you have a good landing spot selected. Be careful to not chip the edges or scratch the defroster lines! Reinstalling is a bit of a pain so I usually like to have a glass shop do it (a small luxury that saves a ton of cursing), but if you're interested in the steps for that, let me know. Be prepared for some frustration, auto glass is the least mechanical and most art-like part of car work, IMHO. Good luck!
Dave

 

When getting the glass re-installed. Make sure that the new seal is warm - i.e. sit it in the sun for a few hours (or HOT water). It is a VERY tight fit over the glass, I've just had my 240Z rear glass installed, and we tore the seal it was that tight.
I've fixed it with urethane, but if it was hot & more supple then it would have gone together much easier.

Ben
Adelaide
Sth Australia
IZCC#1902
240Z L31ETT
L28ET MR30 Skyline
FJ20ET DR30 Skyline RS-X