Rebuilt quite a few of these both manual and electric motor operated. The one in the OP has almost certainly lost (broken or missing) its return spring.
The popular Klaxon ES type are still available new as below, and have a spring inside the square tubing that supports the toothed square section operating rod. The toothed rod drives a geared free-wheeling flywheel that also has a toothed striker on its shaft operating on a central stud fixed to the sound diaphragm.
Note the tight fitting innards have to be removed and re-inserted in a certain order to avoid tears. Carefully note and replace diaphragm shims in correct order during disassembly as well to ensure same tone.
Most other manual horns work on a similar principle to above with the notable exception of a clever design by one Eugene Cowey. He patented a design of manually operated horn using an ingenious course pitch threaded rod similar to a toy top mechanism operated by the plunger. A ratchet mechanism engaged only on the down stroke provides free-wheeling action on a flywheel which contains several steel rollers free to move within the confines of short slots around the periphery. Supported on ball races, centrifugal force when the flywheel spins throws out the rollers that act on a central stud on the sound diaphragm, allowing a very long overrun sound as flywheel slows and they retract. The return spring of operating plunger can be seen in diagram below.