That, but it also looks as if that wire you're holding is a ground wire that a PO might have added to make things work better.
Before you remove the regulator, either disconnect the battery or unplug the connector at the regulator so it's not connected.
Not sure if it will always bugger a regulator or not, but you "can" fry a regulator by running 12v to it with no ground. Not sure how that works, but it's been mentioned here many times by those who know a lot more than me about that stuff.
While it's disconnected, check voltage on the 3-wire connector to make sure the circuits are functioning.
The positions might be marked F, S, A & I. On an EB, only the first three are used. On cars and trucks with lights instead of an ammeter, all four are used in a different order.
On yours, you should have:
1. An Orange wire at F (field).
2. A Green w/red wire at S (stator, or in our case "switched")
3. A Yellow wire (or two) at A (armature, or in our case "always hot")
The Yellow wire (in the regulator plug) should be battery voltage all the time. Check it to make sure it's within a fraction of a volt of actual battery voltage.
The Green w/red wire should have battery voltage when the key is in RUN (but not ACC)
The Orange wire should just have good continuity between the connector and the back of the alternator on it's FLD terminal.
The I position (ignition, or "indicator") is blank
You have a second Yellow wire there that I can see that does not go anywhere. Originally there would have been a capacitor thingy for radio noise reduction. Same thing on the positive side of the ignition coil at the Red w/green wire.
So it's easy to at least test the wires and connector. Not so much the regulator itself.
If you jump a wire straight from the battery to the Orange Field wire (or just from the yellow A wire to the Orange F wire in the connector) you can fire up the engine and see if the alternator is charging the battery. This can be seen by either watching the ammeter go up or by measuring voltage at the battery. Should be 14.5v when the alternator is working normally, but can be as high as 16 or 17 while you have the jumper wire there. So it's not a good idea to run the engine longer than it takes to test the voltages. Batteries don't like overcharging, but can take it for a few minutes without trouble.
If you're not sure about all that, it's also easy to take the alternator in to an auto parts store to have tested.
If all that stuff checks out, likely you just need a new regulator.
Good luck
Paul