This has a pic of the K17 090 08-S part. Can't order it there, but can at least confirm it's the right part. https://www.gdn-industries.com/en/kohler-spare-parts/lever-k1709008s-p884.php
Someone got back to me:
Me-
"https://cc.shankslawn.com/oemparts/a/cut/5b74c16a87a8661288176ac3/kohler-ch440-3204-fuel-system
Item #27
What part is that? I've been looking for a number all over. Thank you."
Them-
"SHUT OFF LEVER.. YOUR USES #7 INSTEAD. THEY USE A GENERIC DIAGRAM WITH ALL THE VARIATIONS SHOWN. YOU CAN ONLY CLICK ON THE ONE USED WITH YOUR SPEC, WHICH IS #7.
WAYNE A SINGHAS
SHANK'S LAWN EQUIPMENT
717.375.4455"
Welp. That's the best I can do. I'm usually really good with that stuff too.
https://www.sepw.com/parts/kohler-1709087-s-fuel-shutoff-lever-kit/
Not a single picture. But its labeled as a "kit". hm
This one looks identical. For $8 I'd be tempted to try it. https://www.ebay.com/itm/Genuine-OE...226234?hash=item289b6bd13a:g:LxsAAOSw-3NfQslu
Update... cause y’all are waiting on baited breath....
ordered the 17 090 07-s standard fuel shit off lever as well as a “water proof “ rocker switch. Installed fuel lever and mounted the rocker on a plastic shroud.
works just fine.