How to reproduce NASA/Langley airfoils for general aviation with long chord lengths?
You are right, such a thick trailing edge is not right. It will add pressure drag unnecessarily – quick fix: Just taper the last 10 or 20 percent of the airfoil such that a thickness remains which is sufficient for structural reasons. You don't want a trailing edge that is as sharp as a knife edge. It has no stiffness left, so it will warp and will easily be damaged.

The more elaborate way: Do as if there would be a hinge at the nose and you close the two sides, just like scissors. That will leave the contour unchanged. The "hinge" location is ideally the center of the nose radius.

Tapering the last 10 or 20% will steepen the pressure rise there and will let the airfoil stall a tiny fraction of a degree earlier than with the unchanged surface contour.