Warning signs on the paint will be right there in front of you. Original coating is butyrate dope. The solvents and pasticizers in dope are constantly evaporating starting the moment they are sprayed. If not rejuvenated often, the dope will dry out, crack, and start to peel away from the fabric. Usually starts as small circles, then progresses to large areas. In the early stages of drying and cracking it can be fixed by spraying with rejuvenator. Once it progresses to flaking areas, you can repair by stripping the dope to bare fabric and spraying new dope. That is practical for smaller areas, but at some point you pass the point of no return where you are better off recovering. That said, I stripped my entire fuselage to bare fabric with a paint scraper in one day, and was able to redope the whole thing so it looked great. NOT a cost effective option if you are paying to have it done.
If the dope is largely intact, the fabric will be fine. Ceconite protected from UV lasts forever.
Punch test is bullshit from the old cotton fabric era. If your IA waves a punch tester at you, get a new IA. If you do have a spot where the dope has been compromised and the fabric is weak, you simply strip away the dope, cut out the bad spot, glue on a patch, and redope it. When stripped bare, any weak spots on the fabric will be readily apparent because they will be discolored. When I stripped my fabric, every crack in the dope showed up as a brown or black line on the bare fabric.
One quick way to check the condition of dope and fabric is to park the aircraft in a dark hangar, put a work light next to the rear fuselage, then open the battery compartment and stick your head inside. Any compromise to the silver layer will be a beam of light shining into the dark fuselage. Very obvious.
IMO the big concern is not the dope or fabric, it is the frame. After 40+ years that epoxy primer is toast if it has gotten any UV over the years. Pull your floorboards and battery compartment and look closely at the lower frame tubes for loose primer, bare metal, or rust. Pay special attention to the area under and around the battery box.
When I bought my 78 two years ago, the frame looked really good. However, when I pulled the fabric off, I was really shocked at the poor condition of the primer. Bare metal frame everywhere. In a few more years I would have had a serious corrosion problem. IMO 40 years is approaching the outer lifespan of the covering, not because of the dope or fabric, but because of the paint on the frame.
