Hey Joel,
Rear bedroom slide is electric, so yes it's just the one living room slide that's got the one single hydraulic cylinder moving it. Believe it's yes also that our setups are totally different. With shared reservoir tank and pump, but separate solenoid block controllers for levelers vs. living room slide, I believe I'm down to simply finding out which SMC Solenoid block controller I have for the living room and securing technical data/instructions on its operation. I did notice on another photo I've attached here markings just above the 2 solenoids. ("E" and "R"). Assuming those stand for Extend and Retract, but again, will pursue finding tech. data on exactly what I have and how to control its hydraulic flow. i.e. to extend would one just loosen the "E" solenoid nut, that nut and the nut on the other end of the block, both "E" and "R" nuts simultaneously with or without nut on the other end, etc.
Unfortunately, didn't see any model numbers stamped on or a sticker on this old unit giving a model number. That would have made it way to easy to find its tech manual. I contacted SMC requesting an email address so that I could send a picture in hopes they would know what I have. So we'll see if any response/assistance comes from that. And maybe someone will happen upon this post that generally knows this solenoid block and how it works to advise what I need to know.