Mark's LED ON state is the AND of two squarewaves. Driving the LED with two PNP's would yield the NAND: LED ON when either or both clocks are LOW. You could add NAND gates and drive the PNP's from them (thus inverting the NAND output back to AND), or you could use a diode AND connection with NPN's. Use a single NPN to drive each LED, but put the LED in series with the emitter and the resistor in series with the collector. Add a pullup resistor from base to Vcc. Now the base voltage is the sum of the LED drop and Vbe. That's high enough to use the base as the diode AND connection. Either clock LOW pulls the base LOW via its diode and turns off the LED. Only the base pullup resistor draws current with the LED OFF. Could use a Darlington to get it even lower, or even a MOSFET like 2N7000 if Vcc is 9v.

Using two NPN transistors to drive each LED results in current being drawn from the battery all the time, even when an LED is off (i.e., when both of its drive transistors are ON). A better approach would be to use two high-side PNPs: connect each PNP emitter to Vcc, each PNP base to a gate driver, and each PNP collector to a 100 ohm resistor