-
Shimano SG-C6001
The tech docs say that it is low normal (ie, release all the cable tension and it'll return to the lowest gear) so you need a 500 series shifter - https://www.sjscycles.co.uk/gear-shifters/shimano-alfine-sls503-8-speed-rapidfire-shifter-right-hand-black/
If you are faced with a shifter and you don't know it's part number you need one where the 8 is at the lever side, the 1 at the barrel adjuster side.
You set the shifter to position 4 and match up the yellow marks at the top of the cassette joint. It's not a difficult process. Removing the cable from the cassete joint is slightly tricky, one of those things where you could do with an extra hand but not too bad. Pays to give it a wee clean before fiddling with the cable so the window for the yellow line is nice and clear.
I've found that any time you disconnect the cable or anything it'll take a wee bit for everything to seat itself back to where it wants to be so don't go fiddling the cable tension as soon as you reconnect it, run it through a few shifts to see if it settles.
-
https://www.youtube.com/watch?v=qpHQdSvLQj8
Pretty good non-verbal video that shows you everything. They are adjusting by the yellow marks at the bottom of the cassete joint, there should also be a pair at the top with one behind a clear plastic window that would be more easily seen (though maybe harder to get on video) once the wheel was in the bike.
There probably is a grip shifter but there's definitely rapid fire ones and they are definitely better.
There are versions of Shimano's 8 speed hubs which shift in both directions so you need to match the shifter to the hub somewhat if you want the numbers to match up.
If you post the part no from your hub we can post links to the correct type of shifter.
If you buy a new rapidfire I think itll come with a new cable and maybe the anchor bolt thing from the end. There are instructions on how far to set that from the end of the outer cable but in my experience it'll always need a bit of fettling to get it dialled in and line up the yellow marks.
If you're going to own an 8 speed hub you'll want to get familiar with aligning the yellow dots as if they get misaligned your hub internals won't last long.