The difficulty with patching this kind of problem is the damage is nearly impossible to stop by just stopping the leak. Commonly, what happens is water leaks into the bunk structure between the outside Filon (or whatever covering) and the bottom layer of the bunk upper surface. It's trapped because there is not way to drain. It can take a long time and a lot of water before the problem gets to the point where you see it as you have reported. Using Eternabond may well stop the leak, but not the continuing damage (rot).
I recommend you open up the bunk structure to see what is going on. This can be done relatively easily by cutting sections of the top layer of plywood to expose the interior of the structure. You should see foam insulation sandwiched between the bunk top and bottom surfaces. It should be dry, of course, but don't be surprised if you find the insulation saturated with water and much of the wooden framework soaked and/or rotten.
If you are lucky, maybe it will be fairly dry and rot free. If so, by using space heaters and/or fans you might be able to dry it out and recover the access holes you cut with another layer of plywood. If you are not so lucky, follow my website link for what I had to do to fix my problem.
In the process of repair, I 1st tried rebuilding and resealing the roof, replacing and sealing the clearance lights, etc. When that did not solve the problem, I rebuilt it again. This time I removed the front window and replaced the entire front portion of the rubber roof (about 4') and sealed all joints with Eternabond.
Even after taking those measures, I still found leakage which proved to be water getting in through the two small side windows in the bunk area. What made it difficult to find was it only occurred when the nose of the MH was downhill (as it is in my driveway) enough to allow the water to overflow the small drains in the window frame allowing water to cross over the ridges the windows slid on. Luckily, when I rebuilt the bunk area the 2nd time I made the bunk top surface removable so I could inspect for water penetration after a hard rain. That little idea saved me from having to rebuild a 3rd time or blow it up.