The local Langlands correspondence for $GL(2,F)$, for a non-archimedean field $F$, gives a one-to-one correspondence between (equivalence classes of) irreducible admissible representations of $GL(2,F)$ and admissible Weil-Deligne representations. However, the correspondence need not be one-to-one always, and the first such case is the group $SL(2,F)$. I understand that the set of representations that map to the same Weil-Deligne representation is called an $L$-packet. After reading the $GL(n)$ theory (Bump's Automorphic forms and representations and Kudla's survey on $GL(n)$ ), what are some good places to find an explicit description of $L$-packets of $SL(2)$ and the corresponding Weil-Deligne representations? I have started looking at the paper on $L$-indistinguishability for $SL(2)$ by Labesse and Langlands.
If one wants to know about $L$-packets of other groups such as $GSp(4,F)$, is it a good idea to read about $SL(2)$ first or is there a more general theory that is more instructive? Any resources or suggestions would be great!