Shelf mounting (asking for a friend)

[Gozo]

A friend asked if I knew what type of bracket these shelves used. He said that he had them up years ago and it was a long strip the notch in the back went in to. Attached below some pics I got.
Being it’s such a long board (and as I’ve found out the hard way in the past), I wondered if there were any center supports to keep it from sagging or breaking under weight. He says “nope”.

Any thoughts on what type of mounting hardware these would use?

 

[Codyboy]

Looks like its rabbeted to fit in a dado that is probably in the back of the book case

 

[morkus]

These are my shelves Gozo has pictured. They were up on my daughter's bedroom wall for many years. They were solely supported by a single rail that the rabbeted edge slipped into. Each rail was simply anchored to the studs. They never had much weight on them but did have a couple of florescent light strips suspeneded. I have no idea where to get the rails as it seems no-one carries them. I realize I could use a different mounting scheme, but would prefer the original if possible, Ideas??

 

[Gozo]

@morkus emailed me that he thinks these are the brackets he needs:
https://www.homedepot.com/p/Dolle-RAIL-0-75-in-Silver-Shelf-Bracket-33150/203530081?

Could be, but from the looks of it, I wouldn’t park anything heavy or valuable on it.