Perhaps I should have, but I haven't documented the BYOM functions, other than the lavish commenting of the code. Struggling with the interpretation of sensitivity analysis is normal, especially when it is a dynamic model that was fitted. I would say that such a sensitivity analysis is, in most cases, pretty useless. But, there will be models and applications were it would be useful, so that's why the functionality in BYOM is there.
What is perhaps helpful is to take a look at the GUTS e-book, Section 7.5. That shows/discusses various sensitivity analyses for a GUTS case study. There is also an example in a recent DEB-TKTD paper (Jager et al, 2023, in the SI, see https://doi.org/10.1016/j.ecolmodel.2022.110187
The local sensitivity analysis is, in its nature, pretty straightforward: relative change in model output per relative change in a parameter's value. Trouble starts when you have many parameters, many endpoints, and endpoints that change over time.