SLICKSALZ,
Hopefully the little battery will run your caller long enough for you. It will certainly save you some money.
You are correct, to measure the current draw you need to connect the voltmeter in series. I'll explain how to measure the current draw based upon the pictures you posted.
First, plug the red lead on the voltmeter into either the receptacle marked 10A or the receptacle marked 300 mA. I would start out using the 10A receptacle because if the caller is drawing more than 300 mA you will blow the fuse in your voltmeter. The 10A receptacle is un-fused, so make sure that you don't short the voltmeter leads across the battery terminals after you have done this it could fry your voltmeter. Then, disconnect the red (positive) wire from the tab in the caller's battery compartment. Next, connect the black lead from the voltmeter to the tab you disconnected the red wire from. Then, connect the red wire coming from the battery to the red lead on the voltmeter. Turn the selector switch on your voltmeter to the A with the solid and dashed lines above it (for measurimg DC amperage). Then, turn on your caller and read the amperage draw measured by your voltmeter. Let us know what your results are.