I do a lot of craft and quickly learnt that there is no one glue. I have a big box of different kinds for different jobs and surfaces.
One thing I use often on caches is sealant. Not sure if there is a more technical name. A clear-ish smelly gel that dries to a solid rubbery form. It’s flexible and waterproof and you can buy types meant for outdoors. I have a cache where a snail was attached and that remains good as new 5/6 years later. Another similar one lost most of the snail, birds I suspect, and all that remained was a snail shaped lump of sealant still attached to the container.
Sometimes basic PVA glue will do the job, or the super glue stuff that comes in two tubes that you mix. The latter is not very flexible though.
I don’t think we have ever relied totally on one thing though. A mixture of glue and, say, wire will often do the trick.
Try out different things, leave it outside as a trial and see.