I have the original version of the Olympus EM-5 (not Mark 1, 2, …) so I don’t know if this is an idiosyncrasy of this version of this camera, Olympus cameras in general or even digital cameras altogether.
When, for example, I take a 4 sec exposure, after the “shutter closes” (sound), it then takes about 4 seconds to save the image to the card and if I take a 20 sec exposure, it takes about 20 sec to save to the card.
Is this typical of the EM-5/Olympus/digital cameras?
Most likely the camera takes a second shot at the same exposure time with shutter closed (dark frame) to subtract it from the first shot for noise reduction.
For what it’s worth, if you’re doing 20 sec. exposures, you may be doing astrophotography. Using my Nikon, trying to get a good shot of the Milkyway, using pretty high ISOs, it makes a big difference if you disable it. Also, this may not apply to your camera though, cover the viewfinder during the long exposures to prevent light from entering there.
There are various test already done on the internet about it and it depends very much on what do you want to achieve and how. The modern sensors from these days do not benefit to much from it, unless they are very heated.
Anyway, in some cases (like time-lapses, or astro where you make multiple exposures for stacking or panoramas) you will not want to have that break between your exposures. For this cases you will want to disable it and take some ‘dark frames’ (exposure with the lens cap on) yourself, at chosen intervals, that you can subtract from the exposures in software.
Mirrorless means electronic viewfinder - so there shouldn’t be any light entering through the viewfinder (of course there might still be light entering through there, that that would just be a build/design defiencency, while for optical viewfinder it’s inherent in the principle).