Bartamos. The only thing worth noting in that mm picture is the mm settings and the red lead - nothing else. The battery is a fake/look-alike so those metal looking plates on top don’t connect to anything. The black lead isn’t actually touching anything in that pic and I had already put the battery charger back on when I took that pic. A new pic of just the meter is attached.
Yes, when I ran the drain test with the negative battery cable disconnected, I had the red lead plugged into the 10A jack and the dial set to 10A. The red lead was then connected to the negative battery cable. When I’d then touch the black lead to the negative battery post, the horn relay would click (I think it was the horn relay but could have been the voltage regulator?) After several times, maybe 8-10, the horn (not sure if it was just one or both) started blowing. I then disconnected the mm and put the negative battery cable on the negative battery post. It then started blowing the horn again. So I disconnected the negative battery cable and put the charger on for the night.
Also attached are pics of my horn relay and voltage regulator. On the horn relay, the brown wire on the right goes to the steering column. The red wire in the center goes to the BAT terminal on the voltage regulator. The thicker red wire on the left connects to the two horns. Thanks again for your patience and willingness to help!