I thought about using carpet... but two things came to mind. One: Boy, carpet with no cushion must be uncomfortable. And Two: The seat doesn't look very Star-Trek Like... Some of my heros have been painstakenly replicating the TOS Captains Chair is this thread on
Yuku's ProReplicas... so I stopped by for some pictures of the seat cushions on the chair. Turns out there is an internet belief that the chair was based upon this chair in the late 60s:

I've never done Upholstry before... but I wanted to give it a shot; so now I have a plan.
I went to Hancock fabrics to see what they had for a simular look. They had some black PLeather which should stand up well. Some research on google as to how to do some Upholstry work informed me that I need some high density Upholstry foam and some batting. Hancock also carried the Foam and Batting. I bought two yards of the black PLeather. 1.5yrs of the 1" foam, and 1yrd of 0.5" batting.
Prior to deciding on the Pleather; I had purchased some carpet padding; to provide a little cushion on the seat and back... with that plan scrapped; I had leftovers - but became part of the new plan. I printed the picture to paper and determined the ratio of top back cushion to chair height. Measuring the height of the Sega chair back; I determined the new top back cushion should be 9 inches.
I developed a plan in my head where I'd fold the pleather over the top and into the seat back by about 3/4". I marked a 3/4" border around the seat back with a blue sharpie.
I started by spraying 3M 77 adhesive on the top of the chair's seat back - covering the black wood with blue tape to prevent the adhesive from getting on the cosmetic wood. I sprayed the
top wraparound area and the first inch or so of the top of the back. The spray adhesive needs to be on both sides; so I sprayed the first 3-4inches of the pleather back. After letting the adhesive get tacky - about 1minute; I carefully positioned the pleather over the top and wrapped it to the blue like I'd made at 3/4". Sorry; I forgot to snap a picture at this step.
I measured a line 9" for the top and cut the carpet padding to the inside 3/4". Spray Adhesive again to mount the carpet padding to the wood.
I cut the Foam to full size. 9" to the blue line from the top and side to side... making sure not to have it overlap into the tounge of the back - IE so it didn't interfear with the sides when they are put back in place. Following the Upholstry video I found via google; I wrapped the batting around the top side of the Foam. I used the adhesive again. I then sprayed adhesive on the top of the padding, and bottom of the foam.

Allowing the adhesive to get tacky as with all previous and future steps.
I then sprayed the top batting and underside of the Pleather and wrapped the pleather around the new cushion - making sure to wet the "bottom" side of the cushion - IE to replicate the midseam on the orginal chair.

Again; too busy wrapping and didn't snap a picture. :doh: