Have you noticed how the fibreglass transition from the air cleaner to the carbies on E-Types is usually damaged where it is Pop riveted to the two internal mounting brackets.
The cause of this problem appears to be that the fibreglass compresses slightly due to the force applied by the Pop rivet. Eventually vibration causes a slight movement of the fibreglass under the head of the rivet. The fibreglass starts to chafe, the rivet holes enlarge and eventually the rivets pull right out.
The fix I have employed is as follows: Drill the heads off the rivets and punch them out. Then, at each rivet position, glue a bush into the fibreglass. The bushes are only as long as the fibreglass is thick (about 3 mm) and have an outer diameter less than the rivet head. A simple fixture can be made to maintain the correct location of the eight holes. I used a polyurethane adhesive (Sikaflex), but an epoxy adhesive such as Araldite should be OK.
After the adhesive has set, scrupulously clean the inner face of the fibreglass around the sleeves. Now glue a flat piece of steel approx. 0.5 mm thick with matching holes over each pair of bushed holes. A bit of zincalume or colourbond is quite OK for this job. Use a polyurethane adhesive (e.g. Sikaflex). The purpose of the steel backing is to spread the load at the fastener rather than to have it concentrated at the point of fixing.
You can now firmly rivet through these holes confident that you will have a permanent sound joint.
A similar technique can be used at the four mounting holes of the fibreglass fan cowling. These are bolt holes, but the same principle applies.