Have you been on the roof yet? If not, head up. They are walkable roofs. They do have a lot of flex in them (this is normal). Being a 2007 and you mentioned there appears to be water damage so be a little more careful, just incase out of view under the membrane there is a lot of rot and a weak spot.
Is your roof the older flat style or the newer arched roof structure (Magnum trusses)? The arched roof structure has a good joist every 24". The flat roof, there is less structure. They are known to sag near the AC unit. Water pools here and sometimes leaks past the AC gasket.
I would start off with a roof cleaning and inspection. Cracks in the caulking will lead to water infiltration. If the previous owner was good at maintenance, you will see lots of caulking touchups (visible by various color of aging white caulk).
To clean, I just bring up a 5 gallon bucket with some dish soap in it. A carwash brush and my garden hose, that I wrap around the AC unit to keep from sliding off the roof. Fill the bucket, and scrub it down, and rinse.
Look for tears in the membrane, and cracks in the caulking. Personally I like to fix these issues once and not have to do it again. So I use Eternabond, it is a super sticky sealing tape, made for this job. Just do not stretchy it, or it will self release. You can use Dicor self leveling caulk. Clean and dry the cracks really well. Apply over the existing crack. Or use a plastic putty knife and remove some of the existing caulk. Never use anything with silicone in it.
There really is no need to roll/brush any type of sealer on the membrane. Just touch up the caulking. The roof should be inspected twice a year.
I would look at the AC unit too. From the inside, remove the cover. Inspect the exposed framing. Do you see any signs of water? There are 4 bolts (1 in each corner) that secure the AC to the roof. These bolts should be just a little tighter than finger tight. If they are loose, water could get in. If someone fully tightened these bolts, the the seal has been fully compressed, and water could leak past. 14 years old, it might be time for a new gasket. It is fairly cheap item. Hardest part is removing and disconnecting the AC. This is a good project to have a helper.
Any location where there is a roof/wall pentation is a good place for a leak. A spot often missed when looking for leaks is the marker lights. Remove the lens, and the mounting screws. If the screw looks rusty, water has gotten in. Apply some new sealant around/under the light. Apply a tiny thin coat that goes over the base and lens interface. This will help seal, and keep the lens from falling off.
FYI, wrap the ladder with a couple old towels were it touches the TT and put your stabilizers down when you go up on the roof. Lastly wear clean soled shoes and remove objects from your pockets. Them membrane is very thin, and tears easily.
Have fun with your new TT
2012 Jayco X23B
2020 Ram Laramie 3500 SRW Air ride 50Gal fuel tank.
2007 Dodge Dakota Quad Cab (retired from towing)
Equal-I-zer 4-Point Sway Control