@iguanaman3, thanks, I should have mentioned I put this thing on the 18v accessory loop with the bubbling oil field and it was some help, but still slow.
I went ahead and took it apart and here are the pictures for the "OGR archive" record. The gap with the vibromotor is obviously too big (red circle). I could see this from the top when you take off the cover to the smoke unit. Like most of these vibrators, there is no adjustment, and something has to be gently bent to reduce the gap. I used a channel lock at the green circle point and gingerly pried up to close the gap. It appears to have worked and now operating faster at 14 volts. The second picture shows the string you mentioned and the entire mechanism.
One final note, when you reassemble, get the orientation of the final linkage on the arm correct. You can guess how I found this out.