I had the same problem with my 60s "spur-lock" hi hat. Basically a Speed King Pedal like clean and lube is the answer.
The pull rod unscrews from the pedal linkage at the bottom. Uses Hex at top of lower rod to loosen and remove the rod (counterclockwise). Use WD-40 as necessary to release the linkage at the bottom.
Disassemble (pay attention to what goes where), remove the spring, rod, linkage, and any other pieces. Spray all metal parts well with WD-40 and let sit for 24 hours. Threads too.
Ramrod the tube gently with small terry cotton towel soaked in WD-40. Inspect for washers, felt, etc wear and replace worn.
Rinse and dry prices. Completely, but lightly grease spring and all moving joints. A touch in the lower tube as well. I use white lithium grease. Reassemble and you should have like new action.
Make sure pull rods are true as well. Roll on felt surface and adjust.
Hope this helps.