Is there a way to increase tension on the cable to fold the seat once it has stretched.Something simple like they use on bicycle brake cables would be convienient to find

One of the cables that control the release is broken right where it hooks to the seat,, the cable has a loop made in from factory it wears threw there,,, this is just one of the causes but the most common,,, also could be bottle cap or small piece of something making it hang up,, hope this helps

Check the cable to ensure it hasn't been stretched. Does it have tension on it when you release it? It should have. A stretched cable will often engage the parking brake, but not release it. This is due to the condition of your hardware in the drum itself. I recommend removing the brake components and either replacing them, or cleaning and greasing them to restore proper function. Check for cracked/broken springs and worn surfaces of course. Sometimes the hangers and mounts for the cable break off or become loose. Inspect those for rust/corrosion. Please remember to use wheel chocks and safety stands when under a vehicle.

There is a cable that connects the handle to the latch, the cables like to break/stretch, sometimes if you look close at the rear of the seat where it attaches to the floor you can see the latch and manually release it with a long screw driver or similar tool.
Cables are avaiable from GM dealer if thats the problem.

Releases in trunk is of no use: no tension/connection therefore cannot engage/pull the cable to release seat to go down. The lever on lower right side of rear right seat won't engage, just flops about.

I just ran into the exact problem with my 2004 Suburban. Once I got the seat to lay down all the other mechanisms worked as they should and I could get the seat in and out as usuall. I found this post below which explained how to get the seat down. Wish I could take credit for figuring it out on my own but I can't.
"After working on it for a couple of days here is what I did to remove the 3rd row seat.
On the rear lower right and left side there are plastic covers, if you push the seat material forward a little you can see a hole where a nut holds it on, remove the nut. On the left side pull back the plastic cover and you can see the wire and the lever that releases the seat. With my foot holding up the #1 release lever on the right side I used an open end wrench to push forward the left side lever and the seat folded down.
I then used the #2 and #3 levers to remove the seat.
To view the whole cable, open the lower seat cover, it is an overlapping plastic clip, My problem was a loose cable, similar to a brake cable on a bicycle, after fixing it I have had no problems."
To remove the nut I used an 8mm socket wrench. My problem was not a loose cable but the #1 mechanism wouldn't pull up all the way, I'm guessing because that left side locked in out of order. I pushed that left side lever down with a hard tool and had my 5yr old daughter pull up on the #1 and the seat folded right down.
Hope this helps if you havn't already gotten it fixed.

Attach cable to brake shoe before mounting the brake. You might have to wedge it in position. After-which adjust brake shoe pressure against the drum. Loosen or tighten adjustment tension nut at the hand brake lever if necessary (before and after).

I have a dealer with some traditional values.Rang up to ask about booking in - could always cancel if fixed - and he said "lift the fabric at the base of the seat where it meets the backrest. In there there is a cable like a bicycle brake cable. Give it a prod, fold down the back rest and then fold up again. This cable makes the headrest move and sometimes it gets stuck". Well, tried it just now - headrest fixed. Total time to implement fix ~1 minute. Great Dealer! Could have ripped me of for loads of money and I would have never known.

Cable is broken or stretched. pick up the bottom seat and see the cable end if broken or slack from being stretched pull that cable and then the back should fold down. Ibelieve you will need to remove seat to repair the cable. the bottom seat when lifted pulls on a cable that releases the backs lock to fold down

There is a cable that pulls the release when you fold down the bottom seat. Broken cable can be repaired by replacing cable.

Loosen the cable nut at the rear brake, pull the cable until the tension is tight, then tighten the cable nut. Since the parking brake only operates on the rear brakes, your rear pads may be too worn causing the parking brake not to hold. Check the pads first to see if they need to be replaced. Also, the parking brake cable can stretch or break over time. Verify that isn't case since you may need to install a new cable rather than adjust it.