Sure we used both sides simultaneously.  It made confessions go more quickly, and there were a lot more people in line for confession.  Above the side doors was a light.  Red meant someone was in there; green meant it was unoccupied.  So we'd line up for confession and go in whichever side was empty when we got to the head of the line.  We'd see the person before us come out (if there had been someone there).  If no one was in line, we'd choose which side we liked--as long as the light was green--and go in there.

On the inside there was a sliding panel which the priest would close so you couldn't hear the confession of the person on the other side or the priest's words to him/her.  If you could hear, you were supposed to put your fingers in your ears, but this happened seldom, at least to me.  When the other penitent was finished, the priest would slide the panel away from the screen on your side and you'd begin your confession.  When done, he'd slide the panel back in so you couldn't see him anymore and the next person, who had been kneeling, waiting for his/her panel to be moved, would begin to confess.

I fondly remember a very devout priest who used to help out our parish on Saturdays for confessions and then on Sundays for Masses.  Sometimes I was the only one to confess, so often I'd go in the confessional and there would be a light on over his head and I'd see him sitting there saying his Office.  I had to wait until he finished before he'd turn off the light and tell me to begin to confess.  He never looked at me.  Just kneeling there, watching him pray--I cannot describe what it did for me, for others.  It just helped us become recollected and more serious when we confessed. We all loved that priest so much.  After Vatican II he was sent away.  No one knew where.  

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In Boston there is a shrine to Our Lady of Perpetual Help, a very beautiful church with about 10 confessionals like the one pictured in the OP, and a friend told me that sometimes they have a mission when several of these confessionals are active.  In years past, they used to fill them all during such missions.

http://www.bostonsbasilica.com/photo-galleries/#.VgeCLitRqzk



At Arcadia SSPX (CA) they have two built-in confessionals with two penitents doors and a light above each door, so after each person leaves, the priest can immediately begin with the person in the other confessional, and he doesn't have to wait for the person just finished to leave and someone else to take the place, because the leaving and coming in happens while the other side is being used.

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Here's a picture of the Boston Basilica that shows 7 of the confessionals from a distance:



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It so sad that some old confessional booths ended up either on display
to be mocked and telephone booths in the Spaghetti factories. Ones
I know are in Dallas and in Houston.