13A Engagement's beginning with flash rock (3) and 20A Beaming head off, do well at golf in the morning (6). The answers look like ego and agleam, but I can't parse them?
I think 13a might be EMO. A genre of rock music, so it seems. First letter of engagement plus mo(ment), flash. AGLEAM looks right. Fits the definition, and (e)agle (2 under par) + AM