When would a sailor always use H after G but without using P ( because P may come before G and H )?

Nobody? The answer is in international flag codes.Flying a single flag for letter G means 'I require a pilot', H is 'I have a pilot on board' and P (known as 'blue Peter') is 'the vessel is about to proceed to sea'.

These are all still in use, as they give a clear, visible, unambiguous signal which is 'broadcast' constantly.In France we see B 'I am taking in or discharging explosives' flown almost permanently on ships in Toulon ( a naval base). In Antibes we used to fly D on our boat so often when entering or leaving port that innocent locals must have thought it was our home port's pennant. D = 'Keep clear of me. I am manoeuvring with difficulty' (Happily, we never flew O, though we were close sometimes. O= 'Man overboard')

Signal flags

I spent some time on this but without success. I looked at sails and ranks and wind speeds - even considered scientific/chemical symbols (P for phosphorous, H for hydrogen, G for unit of acceleration) but got nowhere. I didn't give up though - I didn't flag.