We've got three around the house, two big ones and a smaller one over the fridge. The two larger ones (Blue Moon and Miller Chill) are almost only on if people are over, which is not often, but the third smaller one over the fridge is on 24/7, or damn near. Does it pull a lot of power, or are they somewhat efficient like their light bulb counterparts?

Not usually.  The neon gas "argon"? I forget takes a bit to get going, but not much after that.  I remember working at taco bell back in the day and the manager never gave a shit when we left that one on.

Depends on the size of the tube, length, etc. Neon is fairly effecient. Bar signs, IIRC, use anywhere from 50-100 watts. I could be wrong about that, going from memory.

They waste more in transformer loss than they use in making light.  They are very efficienct in making the light.  Just not efficient in the transformer.

It cools because of the physics involved.  It takes a lot of power to charge up the Cathode inorder to get the first electron to jump energy states.  But once the first one does you've got a cascade of light emission as other electrons bounce of other neon atoms and cause more light emissions.

sorta the same with lasers except you use a flash lamp to excite the laser material and a laser transition  takes more energy to get started but once the cascade begins it's not that much power.

I took a class at a local Neon sign studio and made a "sign" for myself.
Really more of a sculpture, it's down at my mom's house.
It was fun. If you learned how to bend glass tubing in HS chem. class, that's pretty much where you start.
You use an extremely high voltage current to purge the tubes.
The glass glows white hot, it's pretty cool.