How Much Longer will this single track stuff go on?

It will continue until the new station is built, probably six months to a year or so.

Short answer:
Like FormerTO says, - plan on 6 months to a year.

Long answer:
Both tracks function in Automatic, so they could be used. However, the station is under construction, and the workers need some form of access to the station. They drive to the median of 580, and park next to the tracks, but to cross the tracks, they need a special kind of clearance called "Work Orders". Work Orders means that you can walk on the tracks, and Central will keep trains out of that area. For example, you drop your cellphone in a station, and the agent gets work orders to retrieve it. A train can be at Fremont, and an agent can ask for work orders at Union City. The Fremont train (which could eventually reach Union City) will be put on a hold. The TO will acknowledge, and then Central will give work orders. The work orders include an expiration time, and, for this example, it's usually a half hour. In practice, it only takes a few seconds for the agent to grab something with a grabber (even though he is not stepping into the trackway, he is still violating the envelope and needs work orders). Occasionally, he'll walk around from the end, and take about three minutes, max. Once clear, he cancels the work orders.

For a construction site, the work orders are good for eight hours, or so. The workers need to travel between their cars and the site, so they cross the tracks. And, they need to move stuff across the tracks. Occasionally, they will need to cross the active track, and they will get work orders for that. If the timing is bad, the work orders won't get assigned for a few minutes. And, in this case, they only get a short window of time.

Conceivably, when the site is empty (it's usually active from sunrise to about 3 PM, and around 10 PM to early morning), trains could be run through on both sides. I would think that it could be open at these times, but there may be reasons to keep one side closed? Once one side of the sky bridges are in, it may be possible to keep both sides open, and occasionally close one when something large (like an escalator) is shipped in. However, rumor has it that the skybridges were welded with the wrong rod, and had to be rewelded with the correct rod, so they are delayed. Originally, the highway stuff - all the chain link fence, Jersey wall barrier, parking for pickup trucks, flashing yellow - was supposed to be gone on November 1. And all personnel and most materials would come over the skybridge.

The reason your train was held for so long is that probably there were no more trains on one side, or the other. Normally, that should not happen, and, until recently, it was rare. There have been a lot of delays, lately, it only takes one bad train to mess up the timing.