Not sure if you're assuming those 12 shifts are 8's, 10's, or 12's. Basically, in single coverage (or double coverage without overlapping shifts) ED, there are 3 (viable) ways to break the 24hrs of the day. Doing 24 hr shifts (in which case 100% of the shifts will include an overnight component), doing 12 hours shifts (in which case half of the shifts will be overnight), or doing 8 hour shifts (in which case 1/3 of shifts will be overnight).
If you're working 12 shifts/month then 6 of them are going to be overnights (under the 12hr model) or 4 of them are going to be overnights (under the 8hr model).
There are many EDs that don't staff purely for multiples of 24h worth of coverage. Peak times tend to be in the afternoon/evening and so many shops will have someone covering a "swing" shift sometime between noon and midnight. Then there shops that have overlaps in coverage (including my own) that use 9h, 10h, and 11h shifts in some configuration depending on patient volume over the day. These shops are going to have the majority of their physician hours during peak times, and will usually skimp on overnight coverage (and early morning) due to a drop in patient volume that occurs in most shops between midnight and 2am.
We have five 10-11 hr shifts with start times of 7a, 9a, 11a, 6p, and 9p.
I do 13-16 shifts a month and will typically work 3-4 6p or 9p shifts/month. The guy that does our schedule tends to group your nights into 1-2 blocks, with very few/no isolated nights. Usually there will be two days off after the block, although occasionally we do get stuck with a DOMA.
But I'd advise you (if you're interested in EM) to do an EM rotation where you work overnights as part of the mix since: 1) you'll have to work overnights in residency and 2) not working nights as an attending is going to tremendously limit your options about where you practice. On the other hand, if you love nights then you can usually dictate what schedule you work (no weekends or working the same 3-4 shifts every week).