I think if you use a second 555, also connected as a monostable, but replace the timing capacitor with a short (and you don't need the timing resistor)-- triggered by the first one, that should work.

You could also use a D flip-flop such as a 4013 with the D tied high, but you'd need an inverter on the clock and a power-on reset circuit.

I think if you use a second 555, also connected as a monostable, but replace the timing capacitor with a short (and you don't need the timing resistor)-- triggered by the first one, that should work.

You could also use a D flip-flop such as a 4013 with the D tied high, but you'd need an inverter on the clock and a power-on reset circuit.

Or, something like this:

^{simulate this circuit – Schematic created using CircuitLab}

C1/R3/D1 provides a semi-reliable power-on reset (100% reliable if the power turns on cleanly every time after a relatively long 'off' time where +V falls to near 0V).

C2 and R4 provide an edge trigger from the 555 output falling edge.

R1 and R2 protect the CMOS inputs