What's left is whatever your instructor taught you to do when your buddy needs assistance. As the major example I can think of, I was taught how to donate a reg if there is an out-of-air emergency. I wasn't taught how the buddy system can help with a heart attack, so I wouldn't consider that as a factor in using the buddy system. The bottom line is that if you're diving under the buddy system, you stay however close you believe you need to be, and keep however close an eye on your buddy you believe is needed, to do the things you were trained to do for your buddy "in time," and your buddy does the same.
Your failure to monitor your SPG does not constitute an emergency on my part. I can think of very small number of scenarios in which one would "suddenly" run OOG and if that happens they can do a CESA as taught in the class, practiced in the pool, and performed on the exam dive.
Anything else?