Seat Cushion Retainers      -images are thumbnails-
Due to deterioration on the front ,  it is probably a little more accurate to start with the rear seat cushion retainer.   This piece appears to be 3/8" thick and 1 1/2" high,  has a radius to the front,  has beveled ends and is covered with the same light weight material used under the seat cushion. It is definitely not leather nor some heavy topping material;  appears to be more like a lightweight oilcloth.
The retainer shown above has dropped a bit from its original position.  I note that there are no fasteners through the retainer into the front of the seat framing.  It is installed so that it is a blind installation in this respect;  also the method of attachment allows the piece to be lifted up from the bottom with the fabric acting as a hinge at the top.

In the above image,  the strip is tilted forward from the bottom until it is nearly horizontal.   Note that the fabric is quite tight on the wood; I would not be surprised to find that it may be glued to the wood.  The end shape of the wood is clearly shown.
Above image (left)  is a little better picture of the shape and shows the size of the wood strip.
Tape measure is simply holding the scrunched edge of the fabric open to expose some tacks in the top/front of the seat framing wood.  Not clear in the image is the series of tacks which hold the piece in place.   I cannot see any fasteners along the hidden inside edge of the piece nor are there any holes in the face of the seat framing.  The front seat also has some tacks in the same relative locations.  This leads me to believe that the piece was installed as per this sketch:
The upholstery on the front of the seat (leather) precludes one from flipping this retainer all the way over backward on the right side indicating that the retainer was installed prior to the seatback upholstery.  The above image is of the left side which can be rotated backward enough to see what is underneath.

The following images are of the front seat piece.   It is about the same thickness but only a touch over 1 1/4" tall.   This piece has been broken at the right end and is installed now with some nails through the entire piece - wood and fabric.   I believe this is a repair rather than the original method of installation.  I guess that the relatively weak method of installation didn't hold up very long due to the removal and reinstallation of the seat cushion for fueling.