When one is dealing with line-level signals over typical lengths of cable, it's certainly not considered critical to have a large gauge, although one may prescribe to stranded rather than solid depending on their tastes.
You may find more comfort in researching the make-up of the connector itself, making sure the body is made of a quality material such as brass, copper or even something more exotic--the plating is also important. (eww, no nickel please) But once one starts down this path, they begin worrying about the jack, the internal wiring and termination, etc. Never-ending stoooooooryyy, ahhh.. oops, sorry
Oh, I try to use at least 22-gauge, but 24 seems more common. If I make one, I tend to use 16-18 gauge stranded.