Thank you, Midnight, that is very helpful. Given your description, I strongly suspect you saw a large piece of space debris that was tumbling, most probably an old rocket body. Everything seems to fit.
Firstly, it was "flashing" which as you mention, means it would be rotating or "tumbling" which is common for these objects. Secondly, its faintness is about what you might expect for such an object. Thirdly, given the approximate time you mention, the fact it disappeared as it got to its highest point is consistent with the type of low earth orbit rocket bodies tend to be in as they enter the Earth's shadow.
Orbiting rocket bodies are actually more common than you might think, so it's not as if this is a really unlikely explanation. To get some idea, have a look at this site which shows satellites, rocket bodies and large pieces of orbital debris in real time:
http://stuffin.space/
Finally, you may find this interesting. I suspect the reason you wrote "
I could see some looking directly at it, but more consistently by looking just off to the side of the track" is that you inadvertently used a technique called "averted vision". The very center of your retina is not very sensitive in dark conditions whereas the area surrounding it is much more sensitive. Amateur astronomers often use averted vision to spot very faint objects. It takes practice, but, basically, you look slightly away from the object to see it. It takes time to perfect as obviously, your brain tells you to look directly at the object that's a little in your peripheral vision, but after a while, it's a great way to spot things you might not normally see.