Quoted from QuarterGrabber:

I have been using Plastex to repair or recreate plastic pieces. It's REALLY strong too, but not nearly as cheap.

Quoted from Gatecrasher:

Some plastics require glue and others are better-suited for solvents to bond. The model kits we all assembled as kids were injection molded from polystyrene which is another polymer with low chemical resistance. That means that solvents like MEK will dissolve it.
The Testers model glue we all used (and some on here probably sniffed) was not really glue. It's a solvent that melts the polystyrene and allows you to "weld" two pieces together.
Plastics that have higher chemical resistance require actual "glues" to bond them together. The same is true for gluing two dissimilar polymers where one has high chemical resistance or gluing to a non-plastic surface.
PET is polyester and can be glued with solvents. You won't get as good results using epoxy or glue.
Probably the most-widely used PET in pinball is Mylar (which is a Dupont trade name for biaxially-oriented PET film). Soda pop bottles are also biaxially-oriented which is why they are so strong. Biaxial orientation refers to mechanically aligning the molecular chains in two directions.
I work in the plastics industry and mold PET bottles as well as other injection molded and blow molded products.
I use that ABS glue I showed a picture of earlier to repair speaker grills that are molded from glass-reinforced acrylonitrile butadiene styrene which is polystyrene with a rubber impact modifier added to increase the impact strength. Fiberglass is also added to further increase the strength. By using the solvent you are actually welding the plastic rather than relying on a glue to stick to each surface and bond.