Sanity check first: replace the capacitors.
Likely the tube is a 12AU7 or 6SN7, or heck, even simpler than that, 6C4 or 6C5 or the like. It can be checked on a tube tester (which, heh, your club probably has one, or does now).
The oscillator coils themselves should be fine, that's not an aging problem. Do check for shorted caps, in case there are tin, zinc or silver metal whiskers growing out of plating or whatever.
Tim