it seems to be a Falcon freewheel requiring the FR-7. Cost a bit under $7. i have a second bicycle to refurbish (very same bike, except the female version, so I assume same freewheel.
Yeah if I go to the co-op I should pay them something, and it is a few miles, so almost cheaper to buy the tool. The owner of the nearest LBs is a bit grumpy unless you are ready to buy a bike, so I tread going there unless i have no choice.
Edit: NDS has that black "dome" that looks like a rubber seal, but it is all metal and ot removable.