Yep, 2 vacuum solenoids by the LH strut tower in the engine bay. They're very simple solenoids that block vacuum normally, and open to allow vacuum past when power is put to them. I would start there, with a multimeter you can identify if power is making it there (I've seen switches and wiring fail). Then, make a visual inspection of the vacuum lines from those solenoids to the engine, and also from them down to the actuator on the side of the transmission. You can even pull these off and feel for vacuum with the engine running.
Yes, there should be an indicator light on the dash for the diff lock. This is an entirely separate circuit with a switch on the transmission, and somewhat prone to failure, so don't take that as gospel.
And yea, if your front diff and axles are intact, it would be fine to drive with the diff locked with a missing axle. Don't run it in gear with it unlocked, as your center and rear spider gears will be spinning like crazy (which they are not designed to do).