If you touch one voltmeter probe to a solenoid post, and the other voltmeter probe to the other solenoid post (the two large connections on the starter), the voltage reading should be zero while the starter is engaged.

If you are reading 7 volts across these two posts, it means there is a voltage drop of 7 volts in the solenoid.

There should be no voltage drop across the solenoid.

 

You got a battery and cables. Just do a simple bench test.

 

I was testing with the negative probe grounded and the positive probe on the starter terminals. I got 7V at the battery cable terminal, and 7V at the motor side terminal.

When I was connecting a battery yesterday, I noticed a spark at the positive terminal even with the 30A fuse pulled out. The key was off, of course, so I'm wondering what is pulling current through the starter cable. The 30A fuse is in the smaller positive cable that feeds the switches, gauges, lights, etc. After I return the new battery I didn't need, I'll use my multimeter to measure this current draw.

 

Ok, now it is a little more clear what you are doing...

The voltage reading from each solenoid terminal to ground is showing that the solenoid is not dropping any voltage, since they are both the same.

However, he voltage should not be dropping to 7 volts when the starter is engaged.

Sorry to sound like a broken record, but the voltage readings you are seeing indicate that this is battery related, has the battery been fully charged?

Have you tried a different multimeter?

Another issue: the fact that you see a spark when connecting positive cable means you are connecting the cables in the wrong order, the positive should not be touched unless the negative cable is disconnected.

Always connect positive first, negative last.
Remove negative first, positive last.

 

Here is a simple test. Install your fully charged battery, make sure the terminals are clean, turn on ignition, press starter button, hold for 3 seconds, release, touch the battery terminals, see if they are hot.

 

I bought a new Klein multimeter. My old one is cheap Chinese and obviously inaccurate.

It shows battery voltages of 13 or 14 on the two batteries I still have. Both were fully charged though one, the old one, reads 12.3 but it's also clattering the solenoid now because I've pressed Start so many times. This is why I bought the new battery 2 months ago.

Its very difficult to get to the engine end of the negative battery cable, which is why I've been pulling the main fuse and connecting the neg battery terminal first before I slide the battery into the battery box. Once it's back there behind the oil bag, you can't get to the neg side.

I was wrong about the sparking. When I retested today with the new meter, I got very little voltage between the POS battery post and the starter cable. It was like .06 V and it quickly went down much lower. However, with the 30A in the line, the smaller POS battery cable read full battery voltage between the POS post and the cable end. The key is off and no switches are on, but that would seem to me to indicate that something on that circuit is grounded and it probably shouldn't be.
Added info
I ran a mA test there and got 58.9 mA.

 

With the 30 amp fuse installed, the ECM draws some power even tho the ignition is turned off.

 

OK, that makes sense. I've managed to disconnect the engine end of the negative battery cable. I'm reinstalling my new-ish, fully charged battery, then I'll run the simple test you suggested. I haven't noticed the cables in posts getting hot before but I wasn't specifically looking for it either.

 

Yes, the positive post connection got pretty warm. I also installed the battery in the correct order, positive first, then negative. I still got sparking, 12.4v and 59.8 mA between the negative cable and the ground lug on the engine as I connected it, same as I got at the + side last time. Battery voltage dropped to 6v during Start according to the more accurate meter.

 

Don`t know what else to tell you here...

Voltage drop to 7 volts (fully charged battery in good working condition) when cranking indicates a weak battery.