There is no hysteresis in the circuit. The circuit is a window comparator with a wide dead band. However, there is an overcurrent condition with the LEDs. You need to add one current limiting resistor (220 ohms-ish) between the Vcc input terminal and the D1/D2 anodes. Since at most only one LED will be on at a time, only one resistor is needed to protect both LEDs. Other than that, I would not make any changes to the schematic until the basic circuit is functional.
Also, you need to add decoupling capacitors across the IC power pins. Something in the 10 uF - 100 uF range where the red and black wires from the chip enter the vertical distribution rows, and a 0.1 uF ceramic directly across the chip power pins. Trim the leads as short as possible.
A logic chip does not work well as a logic probe, because it does not have precise level detection. Also, hysteretic CMOS transition levels are incorrect for monitoring signals that are supposed to be compliant with TTL levels. A logic probe has a wide dead band so that no lights indicates an output that is not making a *valid* signal.
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