I am an academic neurohospitalist at a large center. I work 7 on/7 off on average. No one actually works a true 7 on/7 off (sometimes 14 on/14 off, etc), but we all work 25-27 weeks per year. In our hospitalist group some people do other things, like stroke or epilepsy or tele consults, so work fewer hospitalist weeks - here, "hospitalist" basically means consult service. You can also hold a clinic on your "off" weeks, and have a few fewer inpatient weeks, but not worth it in my opinion.
You are not going to have time to perform inpatient EMGs while on service at a busy center. If you want to do EMGs, you're doing it in your off weeks. Also, there might be credentialing issues. You likely also won't be able to bill for reading EEGs while on service. I do read EEGs not infrequently, though typically just the sections of interest (e.g. a few hours) and don't bill for it. Ideally, you will ask the epilepsy team for an expedited read and see another patient while they look at it.
What you do all depends on your center and what you can do. For example, I serve as backup coverage for resident clinic (few weeks/year), help with residency and med school interviews, and am involved in quality improvement. I am compensated for each of those, but none are "required" by my contract.
Outside of quality improvement, none of the hospitalists do any serious research.