What time do people tend to leave, with respect to sunrise, for the Mountaineers Route day hike (summer)?

I keep reading about 2 a.m. starts for the regular trail, but that would be easy with a head torch on a trail, with plenty of others also starting at similar times. I would think that if someone doesn't have intimate knowledge of the MR, it could be easy to get lost in the dark.

20 years ago I did most of the MR, on the approach to the East Buttress. I'm pretty sure it was early August, and we started around 5 a.m., and it got light quite quickly (exact details are fuzzy, I remember the time we started, but not exactly which part of the summer. I remember huffing and puffing a lot on the way to the start of the climb!). This time it'll be September, so a later sunrise.

Thanks,

K