Got it to work although the timing is not accurate. Not looking into it rn.
If my + voltage is higher than my reference voltage at - then output at Pin 1 should be High, so for this n channel open drain output, that means
??
It means Pin 1 is floating when HIGH, that is, not connected to anything inside the chip. (you could connect it externally to bias it to some other level but for your application it is just disconnected.)
When the reference voltage, -, is higher than the voltage at the + terminal, the output at Pin 1 should be Low, so for this n channel open drain that means???
It means Pin 1 is connected to Ground inside the chip. Look at the "internal schematic" of the chip in the data sheet. When Pin 1 is LOW it is really low: grounded.
When the output goes HIGH.
No, the output of this comparator never goes high, instead it floats disconnected or it goes low. The LED does not light when its cathode is disconnected from ground.
Yes, that is right. Although the two states of a digital output are called High and Low, in this case High means "not connected internally", while Low means "grounded". Sorry for my confusion, I wasn't looking at the right data sheet.
I have the circuit working on my bench using 1/4 of a LM339 quad comparator with open collector output, otherwise with same values as the schematic in the OP.
Since the capacitor is being charged through a 22 k resistor, it takes a finite time to charge fully. So the length of time the output LED is ON varies a bit, depending on how fully charged the cap was when you took your finger off the button.