I'm not sure when the No Entry arrangement started, probably about 1980ish, when the queues back from the new lights, that replaced the Pennycrofts roundabout, started to block outbound traffic turning in from Weston Road.
But, for a good few years after that, most people knew and it all ticked along OK. Then, more on-street parking started and new, non-local people, who
thought they saw a one way street, started to become the vast majority and it all got a bit fraught.
And 'they' have just left it as it is...
It is the bizarreness of the illuminated sign that might alert most people, without a 'rogue vehicle' to prompt them - and it's a sign that few drivers would bother about anyway. There is a further sign after that, non-illuminated, preventing a left turn into St Thomas Street, also. But, you wouldn't observe these signs, as a driver, unless you had already guessed that you could travel in that direction.
I have a vague recollection of The Gate having a smaller, front car park back then and, for a time, you could sneak through that to circumvent the No Entry, to make use of the lack of a One Way restriction, but it didn't last long, and may only have been doable on a motorbike - there was also (probably) a Weston Road access into the rear car park, again disabled a long time ago.
@BobClay might have a clearer memory of the evolution of The Gate's facilities - or he might not have any clear memories of Gate-related events...