Delay on - Instant off timer

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Oh, so it as just meant to bias threshold to below 2/3Vcc? The way you wrote your post made it sound like the R3 and R5 divider somehow were largely responsible for turning the entire 555 into a JK.

Actually biasing THRES below 2/3Vcc turns the 555 into a Set-Reset Latch. A J-K requires a clock, and is much more complicated.
 
Actually biasing THRES below 2/3Vcc turns the 555 into a Set-Reset Latch. A J-K requires a clock, and is much more complicated.
Whoops readpo on my end. For some reason I read your "set-reset latch" as "set-reset JK flip flop"
 
Another version. This one has a different behavior if Start~ happens twice in a row without an intervening Stop~

 
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