Here's a picture of the innards of my 671. The only visible (to me) difference is the area that the (poorly drawn) white arrow is pointing to. The 681 has a cover of some type over that, and in the 671 it's just a hole. I did rewire it with new cloth wires as found in the original. You might see a slender set of wires. I took out the screw in incandescent bulb and replaced it with an LED.
I'll be investigating the above suggestions now, mote to follow.