When I did a refresher course on the Hawk at Valley in 1980, I was briefed very thoroughly about the need to check that the seat firing handle was fully 'down' in its housing when reinserting the pin. Also that this had to be done visually, not by fumble and feel (e.g. the JP guillotine pin).
Same at Chivenor on the first of the new courses; brakes on, engine shut down, then L00K and replace the seat pin, then the canopy pin.
With a zero/zero seat, it would be utter folly to replace the pins with the engine running - should there be a fire, it might be your only way out!