That's cool but I'm still hoping to get some answers to questions I asked 
Sorry, but Bob's standard answer to questions like these is "It depends" - which is absolutely true!
Okay, maybe a few more details.....
If you don't use the antenna and you are happy being within 4 mHz of properly 10 MHz (I presume that is within in 4 milliHertz), can the system operate in this reduced accuracy mode indefinitely? (For example if you don't have a good place to mount the antenna?) Or is this reduced accuracy mode only available after you have initially established a GPS signal with the antenna?
That depends.
If you're using a surplus GPSDO, you don't know what the design criteria were. Some GPSDOs take a few weeks(?) to learn how the OCXO ages. After that, if they lose the GPS signal, they'll nudge the OCXO along to try to compensate for the drift. Some aren't so smart. The only way to determine how a particular type of GPSDO will react is to try it.
Does a GPSDO antenna need to be outside with line of sight or can it be outside without line of sight, or inside with line of sight, or inside without line of sight?
That depends.
I don't know where you are, but, in general, you need some level of visibility towards the equator. Obviously, outside with clear sky is better. Newer GPSDOs have more sensitive receivers that can often work quite happily through a standard plywood and shingle roof. The antenna also makes a difference. A timing grade antenna has lots of gain and better filtering to help give good signals under challenging conditions. Often they give good enough signal strength that an old, slightly deaf GPSDO works as well as a newer, more sensitive unit. Don't get dazzled by the higher number of channels in the newer receivers. Some of the best GPSDOs around only have a six channel receiver.
Sorry for asking this (I know it's been discussed in other threads but I don't recall the conclusion), but is it better to use a GPSDO 10 MHz sine wave or square wave for a clock input to test equipment (frequency counter, oscilloscope, spectrum analyzer, etc.)? Same answer or different answer when providing a clock input for communications equipment (ham transceivers, etc.)?
That depends.
(I'm enjoying this way too much!) I've found that lots of equipment doesn't properly specify the external standard input. They might specify maximum voltage, but sometimes not impedance and often, don't mention waveshape or frequency tolerance at all. Using a GPSDO as an external reference for communications equipment is even more of a crapshoot. If the equipment multiplies the reference up to a higher RF frequency, you probably need a really clean reference with very low phase noise. GPSDOs almost never provide a signal that's clean enough. You may need some kind of clean-up oscillator that's phase-locked to the GPSDO output to get a clean enough signal.
Last question (for now), what is the purpose of the 1 PPS Output vs the 10 MHz Output?
It varies.
Some systems use the 10 MHz as the primary system clock. There could be a multiplier or PLL to boost the frequency. The 1 PPS might be used as an time-of-day / elapsed time sort of thing. They could also use the 1 PPS with a phase-lock loop to lock the system's internal oscillator to the GPSDO.
Bottom line on these surplus GPSDOs is that we really don't know how well they'll perform until somebody buys them and starts doing tests and measurements. That's the way it will always be. That's the value of a forum like this. Everybody can share their test results and build a picture of how well multiple units work under multiple conditions. The alternative is to pay many, many dollars and buy new units straight from the manufacturer. Then you'll get a full set of specs and can ask the manufacturer all the questions you want. But, even then, don't be surprised if you get a few blank looks.
Evil Ed
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