Step 1: Dissassemble!
umm, rip the guts out.
Sorry to be a bit terse, but that's what I did. Perhaps a bit more detail could help. The head of the toothbrush is cut off with a pair of wire cutters. The guts of the toothbrush were extracted. A pair of needle nose pliers was used, but it could be done with most any pointy object on hand. This toothbrush was cheap, very cheap. Did I mention it did not function out of the box? And yes, the battery was good, 1.6V.
Step 2: Soldering
I did change from the 1 fresh battery which came with the toothbrush to 2 nearly dead batteries, about 1.3V each. Two batteries gives a bit more juice, of course, but also makes a symmetrical, balanced assembly.
Step 3: Changing a "spring" Into a "Switch:
Then, use a pair of pliers to contort the spring such that it tends to press against the end of the battery. The bot should now hum away happily, and proceed to terrorize cats and other household fauna. A simple piece of paper breaks the connection.
I have a brief video, but You tube is down tonight. TBD.
This one goes faster than expected, but tends to spin. I trmmed some of the bristles, changing the behavior. You mileage may vary.