Thanks for the tip on the voltmeter, I tried both settings, but used the AC setting for the picture I took. I'll have to fix my voltmeter and try it again.

I noticed that if I put the leads on the button battery, the needle would slowly, but very visibly, go down the whole time I held it on there. When I held the leads to the cell battery for a long time, the needle never moved. Also, I've been messing with this flashlight all day long and none of the readings have changed at all, no matter what I've done.