The damper is a light duty shock absorber. It is oil filled and, once they leak and dry out, the piston hangs up inside of the barrel and drags, making the steering very heavy in both directions. They cost less than $30 bucks and can be swapped in about five minutes - a perfect winter/spring job. To test, you can release one or both ends and see if the steering gets easier (yes, the steering wheel might flutter without it, but it's a test, right?) They probably should be replaced on Speedsters ever ten years or so.
Steering Box Access: IIRC, the original VW steering box access cover was about 4"-5" in diameter with a tab on the inside bottom that caught the inside of the hole to hold it in place, and another tab on the outside top, farther out than the hole, that had a hold-down screw in it - pretty simple. It was positioned in front of and slightly off-set towards the top of the steering box so you could access both adjusters and the filler. I would probably look for a cover that has a couple of hold-down tabs or is oversized enough that you could screw through it into the fiberglass outside of the hole.
But before I started cutting a hole into the battery/spare tire well to get at the steering box, I would find a suitable cover about that size at a Hardware or DIY store and then make a hole suitable for the cover size. 4"-5" or so seems about right.
Remember that the steering box has a filler hole on the top, as well as an adjuster screw, but there's also a big adjuster with a BIG locknut (36mm?) on the front of the box. If you put a portal above the box it will still be difficult to get to the front adjuster.
If enough of you are interested in doing this during the winter, I could get out there and measure Pearl and provide that to the group to replicate (I have not yet made this mod). I'll see what I can find for potential covers at ACE, Home Depot or Lowes and let you know (a last resort might be West Marine).
You can easily make the hole with a 4"-5" hole saw as Ron showed, or you could use a Dremel with a grout cutting tip or a 3/16" rasp and a hole cutting tool (used for cutting holes in ceilings for recessed lights) or even a saber saw as long as the cutting tool doesn't hit the steering box.