Wooden rims went out of style for road bicycles when rim brakes came in, but continued to be use on the track well into the '40's. Similar wood-rim wheels, when overstressed, would suddenly turn into a cloud of sharp, dangerous splinters. There is a third type of valve, very rarely seen, which has a bottom similar to a Schrader and necks down to about the size of a Presta . Woods valves were formerly popular in the British Isles and Asia. You can pump them up with a Presta pump.
Older versions work with rubber tubing and spit.
You should see a short length of rubber tubing covering the inner part of the core. If the rubber tubing it old and perished, the valve won't work. Some patch kits include short lengths of replacement rubber tubing for this purpose. When installing new tubing, lubricate the valve core with spit before slipping the tubing in place. Newer versions use a modern spring-loaded valve mechanism.