I had never heard of the one at Hamilton Square being used until fairly recently when a profound electrical failure stopped operation of the lifts and people were let out via Shore Rd.
I remember using the one at Hamilton square sometime around 10 years ago or so. I think it was an electrical failure back then too.
I did not even know the passage existed until that incident.
Back then I used to work late evenings in Liverpool and as I recall I was on my way home and it was around 10pm on a cold Winter's evening. When I came out on to Shore Road, for a couple of minutes I honestly didn't know where I was.

I just didn't have the familiarity with that locality that I have nowadays. I was also really surprised at reaching street level without seemingly having gone upwards very much. But of course, Shore Road, being nearer to the river is quite a bit lower down than Hamilton Square. If I remember rightly, the entire passage was tiled with really old-looking tiles, but it was so long ago, I can't exactly remember it that well. How unfortunate I never had any digital camera or phone back then!
Those were the days I very often used to use Hamilton Square, before most of the major bus routes in Birkenhead were diverted away from the Woodside bus station, and now instead use the Birkenhead bus station. Generally, it just doesn't make much sense for me to alight at Hamilton Square nowadays.
As for the James Street station Water Street entrance, I have walked past the doors on many occasions, but as it happens never at peak time. I always did wonder about those doors, since I've only ever seen them closed. Now you've answered my question. Next time I happen to get the train home from work, I might try going that way, to see what it's like.
