Jerry most likely has it right. The simple compression of the backrail felt, under the back of the key, may let the whippen drop down far enough that the parts are making contact. That, and compression of the felt directly above the capstan in the abstract-lifter (...if the action design I'm thinking of). If your whippen and backcheck are moving when you touch the key, and the hammer is NOT moving immediately, then lost-motion adjustment may cure it.
With that age; you may need to regulate the hammer rail forward a tick, keydip, let-off....oh you know...the whole drill...to get it working as nicely as possible.
Quick and dirty? Pray that lifting the capstans and removing lost-motion will cure it! If the hammers are checking into the backchecks too far from the strings, you may be able to just adjust the backchecks forward with a finger and both remove the 'click', and get a better responding action.
Jeffrey T. Hickey, RPT
Oregon Coast Piano Services