In my experience, instruments that are meant to use a 10MHz reference clock signal input have their own local oscillator of much higher frequency and the 10MHz serves to keep the local oscillator phase locked to the 10MHz signal. Ultimately then the precision of any timing obtained is up to the precision of the instrument and depends little on the 10MHz signal being either a sine or more like a square wave.
Think of the 10MHz reference input as keeping the local oscillator from drifting at a slow rate like one second per day. Instead the local oscillator stays locked in phase to the reference input.
Most important is when using two separate instruments and having them share a common 10MHz reference signal. This keeps the two instruments in phase with each other. Otherwise depending upon the stability of the separate local oscillators there will be some observable drift over time.
In summary, seeking 2ns resolution, do not look to the 10MHz reference to give you the precision. Instead the high precision will come from whatever clock is used as the internal local clock in the device. The benefit of using the 10MHz reference from GPS then is that you are locked to the very stable atomic clocks used in GPS so you will not see your local oscillator drift slowly over days and months and years.