And it's sort of off topic and very much a matter of preference, but even if you think a logic probe is an essential tool for your kit that you want a quality version of..... if there aren't any available and you just need to check oscillation, a basic circuit and a breadboard will do just fine.
And honestly, if I've gotten to the point that I need to know if the oscillator is working right, I'd much rather see the waveform on the scope and getting a probe out of the drawer takes about as much time as booting up the scope. I've had access to a logic analyzer since I was a kid (my dad was into electronics too), but I never bought one for myself. A simple circuit, a multimeter with an AC mode or a duty cycle readout, or a scope or other simple digitizer all will suffice and it's very rare that I want to see only the binary signal on a single bit (logic analyzer isn't worth it then) and don't care about the waveform, so I haven't found the need for it.
Anyways, it's neither here nor there, in a pinch (it sounds like the OP is in one of sorts) building the circuit to check basic operation is an option. If you then choose to have and use a logic probe, go right ahead. Even a spare micro would do in this case, just reading off a pin and displaying it over a serial port would give you a good idea if there's activity.