You want to know what kind of rubber you have. On older roofs it's not EPDM, however, by 1996 it probably is. My roof is TPO rubber, it has a rough texture and looks kinda like vinyl. It should be coated with elastomeric. Elastomeric can be purchased at Lowes or Home Depot, EPDM cannot. If the original rubber was smooth it's almost certainly EPDM. Yes, that rubber will stick to DRY wood. If it's wet or will get wet then it will not stick, or stick when you apply it then if there's a leak in the future it will let go.
You can buy EPDM liquid rubber in the five gallon can.
https://secure.websolhost.net/@epdmcoatings/order-v2/
It's over $300.00 bucks but, that's cheap when you price it at Camping World. The biggest thing is, before you put anything down be sure that the surface you're working with is bone dry and as clean as you can make it. Otherwise you're wasting your time and money. The liquid rubber is messy. I covered my roof a few years ago because I was told by the PO that it was EPDM and I didn't know the difference. It didn't last very long--at all.
Anyway, I'm real familiar with the process. Get a corded drill and a mixer. Mix in the components in the liquid rubber and stir it with the drill and mixer. Don't use a cordless drill. It will die before it gets the rubber mixed. Then apply the rubber to the roof with a roller on a long handle. Wear old clothes and old tennis shoes because they will be utterly ruined in the process. Take your time but, not too much time. There is a window of working time before this stuff will get real hard to manipulate. You can put it down and when your done, if it rains it wont matter. Rain won't effect it even if it hasn't set up. Check the edges of the roof really good for cracks. Some people will tell you to put down eternabond tape over cracks and then the liquid rubber. This doesn't work as well as just putting the rubber down by it's self. Over the years the rubber will dry out and want to crack around where the tape was put down.
I did a 28 foot with a five gallon supply. I had one gallon left over. Put that in a container and put it in the fridge. It wont harden in the fridge for a very long time. Once a couple of months have gone by and the new rubber roof has completely dried get back up there with the extra gallon and a paint brush and go back over areas that look like they could use an extra coat.
Caution: EPDM liquid rubber likes to bubble. You must work the bubbles out with the roller as you apply. If you don't then those bubbles become little holes and will suck the water in and under the new rubber. When in doubt keep working with it. If you go through a snow storm then as that snow melts you'll be amazed at how much water will get through a few pin holes.
It's summer so, don't try to put the liquid rubber down in the heat of the day. It's just too hot for you and for the rubber. Get up early and as soon as the roof is dry put the rubber down.
The good thing about a rubber roof is that you can always touch up places that you're not happy with. I get on my roof every six months with a can and a brush and touch up any place that looks like it's even slightly considering being a problem in the future. EPDM caulk can be purchased at camping World and is good stuff to keep on board just in case.