Maybe a stupid question; if you're using GNSS as a time source, is it difficult to get reception? Do you have to put the receiver near a window or something? Or is it able to get signal even in cases where, for instance, my GPS watch would fail to get a lock?
Imprecision in GPS (GNSS in general) solutions comes from a number of sources: Orbital errors in the satellite ephemerides, atmospheric distortions to the signal, multipath at the receiver antenna, and a bunch of minor stuff we're not gonna worry about. Those are the big three.
Orbital errors, you can't do anything about. Post-processing allows _position_ solutions to be corrected once the errors are known (a process that takes hours or days after the fact, to work back where the satellites must've actually been) in a process called Precise Point Solution, but that doesn't apply to [this kind of] timing.
Atmospheric errors you can kindof do something about. Signals from satellites lower to the horizon take a longer path through the atmosphere, so they tend to have wackier pseudoranges. Most timing-grade receivers have a default "elevation mask" of 15 or 20 degrees above the horizon, to simply not even bother with these crap signals, and derive timing only from what's left. (There are of course atmospheric models and corrections to apply, but these are applied to everything. Still, start with a cleaner signal and you'll end up with a cleaner result.) This means you need clear sky view to the middle of the sky, in order to raise the chances of an adequate number of satellites passing the elevation mask.
Multipath is huge. The reason survey-grade antennas have these enormous choke-ring structures around them is to eliminate multipath reflections off the surface of the ground below. Even cheap little antennas try to be more sensitive to signals from above than below, to limited success. (Especially if they're wrist-worn and thus not orientation-controlled. Ugh.) Any situation where the antenna is subject to multipath will have demonstrably worse precision as a result. So, most timing antennae are considerably elevated (gives the reflections an opportunity to fall apart), shielded (choke-ring mounts), or both. Cellular sites usually go with the elevation option since there's already a giant lightning-rod nearby, elevating the GPS antenna doesn't come with additional risk for the receiver.
Worse GPS reception means the receiver has a noisier signal to start with, and can't discipline its local oscillator as tightly. Even if you don't care about nanoseconds in the final application, you probably do care about _holdover performance_. And if your LO can be disciplined with nanosecond-accurate signals in the first place, it'll hold millisecond-accurate timing for days or weeks in a GPS outage. If the disciplining process is crap, the holdover will also be crap.