How many words for glue are there?
> pattex?
Never heard of that, but I see Pattex makes a LOT of glues for the German/Euro market. Classic Pattex is a "contact cement", you spread it, let it part-dry, and press? Such glues may not stick well to a plastic LED, but might stick well enough. If you have it, try it.
> I've seen people use hot glue...
I've had trouble with hot-glue (polyethelyne rods melted and shot from a special hand gun) not sticking to big cold metal.
> Araldite
Never heard of that either. But Araldite makes a LOT of glues: car brakes, DVD layers, pipes. Their "DIY" range seems to be 2-part epoxies.
> clear 2 components glue (2-Komponenten-Kleber) (2-components adhesives)
Probably "epoxy", "Epoxid", the most common 2-part home glue. If it is 2 tubes that you mix 50:50, it is almost surely a filled epoxy. Polyester resin is usually a big can plus a very small tube of "hardener". Resourcinol is a purple liquid and a dusty powder (and I have not seen it in years). Plastic water/sewer pipes are joined with a cleaner and a glue: a 2-step process but not really a 2-part glue.
Good epoxy on a clean surface makes a very strong bond. Epoxy on paint will pull the paint off, and most epoxy won't cut through grease or oil. Even a fingerprint can weaken the joint. And some household epoxies are mostly filler, very little epoxy. Pure epoxy is very expensive and not very strong (and not mixed 50:50), usually you want some filler for strength (and to make a nice 50:50 mix). The metal-filled epoxies like Plastic Steel can be very strong (but Plastic Steel is slightly conductive). The yellow epoxies can be very strong or very weak. The clear versions may be less strong. The 1-hour epoxies are usually less strong than the 12-hour stuff, though I once had some great 1-hour epoxy. In fact all these strength values really depend a LOT on the brand and age: most consumer epoxy is very lame stuff, some brands less lame than others, and old (unmixed) epoxy is weak epoxy.
> Goop
Yes!!!! Shoe-Goo (one version of Goop) will fix almost anything. If you don't mind mess and smell. It is the home version of the nasty glue they use to make all shoes today: most casual and athletic shoes are glued-together, very little sewing.
Shoe-Goo used to be better. They used a very nasty solvent which made it easy to spread and would bite-through dirt and oils. And if you sniffed the fumes, it would make your mind fly and your liver rot. Some years ago they switched to a smaller amount of a less-nasty solvent, and now Shoe-Goo is stiff, hard to spread, and does not grab so well. I still use it for almost everything. Transformers, pants, LEDs, wood trim, wall-hooks.