If you want to try using a flip flop, here's one way. It's more involved though than using a toggle switch and passive circuit.
The button is an ordinary momentary NO push button. R3/R6 set the pulse duration.
You can add LED indicators in parallel with each coil to indicated status (as long as it doesn't need to be fail safe).
The CD4013 comes with two FF in a package, so I used one to square up the PB input signal.
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