The 'sensor' is the vapour pressure of the fluid which is commonly called just ether. It can be difficult to get hold of, but has been available in 99p shops as a coldstart spray can. {alas no more 99p shops}.
The thing in the visible gauge is a normal Bowden pressure meter (?) , quite similar to the oil pressure half.
I've been meaning to do mine for ages, but not done so yet.
The bulb end needs to be about half full, (not full, which would measure thermal expansion of liquid instead of vapour pressure).
Depending on how much capillary tube is still connected to the bulb, my proposed method of repair would be.
1 get some ether in liquid form in say a glass surrounded by ice.
2. warm the bulb to drive out some vapour then cool it with the tip in the ether so that it will suck in the fluid, repeat until you think it is about half full.
3. keep the bulb in ice until ready.
It would be all too easy for solder to block the capillary entrance so:
4. get a piece of brass (rod, round or square or hex) about 2 inches long and drill a fine hole lengthwise which is a close clearance hole for the capillary pipe.
5. poke the gauge end of the pipe about an inch into the hole and solder it in at the rod end.
6. keeping the bulb cold, poke its end of the capillary tube into the rod until it almost meets the other part of the capillary tube.
7.Solder it in at the end.
The above process should keep the solder away from the tiny hole in the ends of the tube.
Test by dunking the bulb into boiling water, carefully.
Or
Send the whole thing to Speedy Instruments (?)
or buy one of those mentioned above.