Thanks for the interest and help, Mc Giever.
The chain set-up for the system of opening ash-pit door while closing flue damper door resembles the last illustration in that PDF; but my system doesn't use a lever on top of the furnace. It uses that damper motor, instead. BTW, not seen in the photo, there is also a spring attached to the chain so that if power goes off, that spring will tug the chain back down, closing the fire-pit door while opening the flue-damper. This action shuts the furnace down.
In the photo I posted, the damper motor (with the orange label on its side) has now finally died and no longer runs. When it did run, it would spin twice, moving the chain up-and -down about seven-inches. In the photo, the chain heading down from the sprocket at 6-oclock goes to the fire pit draft door; while the chain heading off at 8-oclock crosses the top of the furnace, angles over a small pulley wheel then travels down to and opens/closes the flue damper. An upstairs room thermostat activates the damper motor.
For the last few days I've been tugging the chain up-and-down manually to speed and slow the burn. At night I've been closing 'er down completely. Thankfully it's not too cold here in Frostburg ....yet.
I need some sort of thermostat-controlled motor to move the chain up-and-down. Yanche's motor with the levers and direct thermostat connect reads to be the closest cousin to what I need. Attaching the chain to levers would work.