Your brushes are the early type. The inside brush originally grounded through the three steel screws to the stator. It also had a black wire that ran up into the harness ground.
The way it is now the three nylon screws unground the brush from the stator. The nylon won't carry electricity to ground.
On your set up by the reg/rec is a plug connector, This lets you unplug the reg/rec. Unplug it.
Now on the harness side of the plug find the green wire. Use you multimeter set on a low ohm scale. Touch one probe to the green wire in the plug. Touch the other probe to the green wire at the brushes. You should get a low ohm reading. At or very near zero.
Now move the probe from the green wire to the body of the stator. This should give you a very high ohm reading, infinity would be ideal.
This indicates the green wire is connected to the brush and is not shorting to ground. This is good.
On the other brush touch one probe to the black wire at the brush and at the brown wire in the plug. This should get a low ohm reading. Move the probe from the black brush wire and touch the stator. An high ohm reading here as with the green wire is good.
This shows the black wire brush is connected to the brown wire. It also shows it's not shorting to ground.
If in either of these tests you find continuity, a low ohm reading, from the wires to the stator, you have a short to ground.
This will blow the fuse.
At the brushes with them removed use the lowest ohm scale on your meter. Touch the probes together, remember the reading you get. This is the ohms of the test leads.
Now touch one probe to each slip ring on the rotor. You can easily reach one ring through the opening in the stator. You need to reach through the brush mounting hole to reach the other. You might need to remove the brush holder to reach in better.
You should get a reading of about 5 ohms, +or- 10%.
When measuring low ohms You check the ohms then subtract the ohms of the leads from the test reading to get actual ohms.
As an example, one of my meters the leads test out to .7 ohms. If I use this to test a rotor and get a reading of say 6.3 ohms. I would then subtract the .7 from the 6.3 and get 5.6 as an actual ohms. This will be well with in the 10% tolerance.
Your numbers will be different.
Also check from the slip rings to the body of the stator. This should be infinity also.
On the brushes Are they both about 3/8 inch or longer? The wear limit is 1/4 inch but they often fail before they wear that far. I think this is because the tension of the spring gets so weak it can't push the brush against the sip ring firmly. Thus losing good contact.
With the reg/rec unplugged turn on the bike and check the voltage on the brown wire on the bike side of the of the connector. Should be at battery voltage.
Try these tests and report back what you find.
Leo