The times displayed on those clocks is available here: http://apps.mta.info/traintime/ or via the official app http://web.mta.info/apps/subwaytimeapp.html
Unless you are on the rare above ground station this is the general layout.
Not to sidestep your question, but do you live in NYC and not use the unlimited pass? I'd assumed everyone did.
http://www.nytimes.com/2005/06/20/nyregion/on-l-train-driver...
http://www.nydailynews.com/archives/news/conductorless-train...
http://nymag.com/daily/intelligencer/2009/02/subway_riders_s...
The plan was to take out even the operator, but unions kept the train operator in. http://www.nytimes.com/learning/teachers/featured_articles/2...
How about retired people or people on a fixed income that are not work commuters?
How about someone that works in their neighborhood but still needs to use mass transit occasionally?
How about students that largely don't leave their campus tether but still need to use mass transit albeit less frequently than a commuting professional?
How about someone who bikes as their primary means of transit but still needs to use mass transit infrequently?
Its not really unusual at all is it?
So if you can't afford or don't need to purchase an unlimited subway that's your problem?
No surprise with the L train as its the only one that is automated(despite having a conductor on board.) They refuse to let it run un-manned which begs the question why did they spend the hundreds of millions of dollars to automate the line? There are plenty of places with unmanned subway lines. There's one in Tokyo and I believe Barcelona and Copenhagen.
I guess its no surprise that their API would be mess as thats about sums up the culture at MTA from what I can tell.
The MTA is spending hundreds of millions of dollar to put arrival clocks in all stations. The problem with is that I want to know how long it is before the next train arrives before I pay for a fare. I have to pay for a fare in order to go onto the platform to find out the next train won't arrive for anther 20 minutes. At this point I have needlessly paid for a fare and generally walk back up stairs and take a taxi.
When they were questioned about this poor decision they responded it was because of terrorism that they couldn't put train arrival times outside the entrance. That makes zero sense.