How do I pack a mod correctly?

Yeah, seems correct.
If it's breaking, that means your modification itself may have problems in it (jbeam file being invalid, wrong syntax or so).
The console should give you hints in regards.

Also note that if you plan to release it, you should make sure that your jbeam does not replace the original ones (give it a custom name, and make sure it only contains your custom part).
This way you reduce the chance of it breaking the vehicle when we push updates, as you won't be overwriting the original parts.