It will vary from company to company and ball to ball. Some, especially smaller companies like Morich and 900 Global, will simply not make lighter weight balls. Others will put a different core in lighter balls.
Storm has made a lot of their older Master line balls (back in the X-factor and Paradigm days) with a simple lightbulb core in the 12 and 13# versions. Track used the core from the Crunch Time in a lot of their higher end light weight balls that had fancy asymmetric cores in the heavier weights.
Other balls from Storm and Track simply weren't available in 12 or 13#.
In the end, if you need a light weight ball, there's no real rule that you can go by. You can't say "Oh, I'll just get a ball from Company X since they put real cores in the light balls". Sometimes yes, sometimes no. As you said, Brunswick seems to be pretty good about publishing that info for others you might have to contact the company to find out.
SH