What are users doing for making narrow, dark accents for cork? I have been using old fashioned black automotive gasket material but not always satisfied how it turns. Are there any better materials for making dark narrow accents?

EVA Foam or burnt burl cork rings. You can get EVA sheets in different colors and thicknesses at Hobby Lobby or other craft stores. Here from Amazon.

[www.amazon.com]

This also works quite well. [knifemaking.com]

You already mentioned gasket material...that comes in black paper and also rubber. You can also use thin plastic material, EVA.
I will usually just go with the black paper...once its epoxied it goes a little darker.

For ultra narrow, black lines between cork rings use TiteBond III colored with black marbling dust from VooDoo Rods.

I see a couple items here that might be worth a try. Thx.

There is also rubberized cork gasket material that gived a bit darker accent than similar burl cork and it comes in colors depending on the material the cork in mixed with, be it Viton, or some other material.

I think I read about using vinyl tile many years ago. Soft enough to sand, but durable, too.

Plastic poker chip? Old black, checkbook cover? Credit card (white).

The auto gaskets would be very thin! Great suggestion by others!

My cork jig can cut a wafer to about an 1/8th inch. Sometimes I will sand it down on a block a bit thinner. (Can get a little fiddley and uneven if not done slowly and evenly.)
Not super thin, but relative to the grip length, it can look great.

Thinnest thing I can think of is my patience! Ha!