Reviving this old post. So, I couldn't get the datasheet for this BJT, however I identified it, using a multimeter, as a NPN. After that, I searched for a package name and searched for other NPN BJTs on Mouser with the same package and ordered a couple. Analyzing the datasheets, they are rather different from each other and I had one working well, one somewhat working and the other two barely work (in terms of the nebulizer unit working). I've noticed that the one that works best has the highest transition frequency and the highest minimum hFE, however it is described in the datasheet as DC gain and this circuit is working at 1.6MHz.
Instead of keeping purchasing other BJTs blindly, I'd like to simulate the circuit in LTSpice and "experiment" with different transistors. However, after copying the circuit to LTSpice, the output doesn't oscillate. Here's the circuit:

And here's the simulation result:

Can anyone point me in the right direction ?