Original 555 timer transistor output implementation
Here is something to try.  Q20 wants to be a phase splitter.  You can read about that here;  enter link description here.  Because you are tying Q20's base directly to 9V it is not working like a phase splitter.  It is two forward biased diodes BC and BE.  The means both the base of Q21 and the input to the 200 Ohm resistor are at 8.3V.  So try this, put a resistor between the switch and Q20 base.  Size it to get say 1V at the 200 Ohm resistor.  When you do this, you will get about 1.5mA flowing thrugh Q20 emitter.  This same current will flow into the collector trying to drop about 10V in the 6.8k resistor.  Since it can't the transistor will saturate at maybe 1.1V.  Now you will have Q24 on and Q22 off.  Driving the base directly with 9V has them both on.