The thermometer is not full of mercury and air, it only has mercury. The air was excluded from inside of the thermometer during the manufacturing process. Where mercury isn’t, there is a near perfect vacuum. This means there is no gas pressure above the mercury to push the mercury BACK down and no gas pressure keeping it from flowing down into the bulb. Liquids in an evacuated glass tube act much differently that they do with air in them. Seal a larger diameter tube with some mercury in a vacuum and tip the tube. The mercury will run down the tube and hit the sealed end with such force that the glass will break like you hit it with a hammer. There is no air to cushion the mercury at the end. If it does not break, it feels like …. well someone hit the end with a hammer. It’s a very odd feeling.Mercury and other liquids have a property called surface tension. This is an atomic level attraction between atoms and molecules. Mercury’s surface tension is very HIGH. A drop on a table will contract into a tiny sphere with a flat bottom caused by gravity acting against this force.

So the constriction at the bottom is small enough that the force of surface tension wins over gravity, but just BARELY. Shaking, or more precisely, applying centripetal force, in addition to gravity, together wins over surface tension and the mercury is FORCED back together with the larger reserve in the bulb. This would not be possible if any air were in the tube separating the two.

I’ve never though of this before, but it is likely a mercury thermometer would not work PROPERLY in orbit. You might not be able to shake the thermometer hard enough, and might have to put it into a centrifuge to reset it.