Howdy
A picture is worth a thousand words dept.
Here is a photo of the internal parts of a Colt Single Action Army. The parts inside an Uberti will be similar. There are three cocking notches on the hammer of a Colt or Uberti. You can see them in this photo. The notch at the top is the so called 'safety cock' position. The notch the arrow is pointing to is the half cock position, and the notch all the way at the bottom is the full cock notch.
The 'four clicks' happen
1. When the hammer is pulled back to the 'safety cock' position.
2. When the hammer is pulled back to the half cock position.
3. When the bolt pops up against the cylinder (the bolt is the funny looking part with the hole through it)
4. When the hammer goes to full cock.
The other arrow is pointing to the sear, which is the upper tip of the trigger. The sear pops into each of the notches to hold the hammer back.
1. Notice the sear is very, very thin.
2. Notice the 'safety cock' notch and the half cock notch each have an over hanging lip over them.
When the sear pops into either the 'safety cock' notch or the half cock notch, it is trapped by the over hanging lip. You cannot pull the trigger unless you cock the hammer further.
However you can break off the overhanging lip or the sear by trying to pull the trigger very hard in the 'safety cock' or the half cock position.
Also, if somebody has done a crappy trigger job on the gun, the sear often does not pivot far enough to clear the over hanging lip of the half cock notch as the hammer falls. In this case, the over hanging lip will strike the sear as the hammer falls. Do it enough times and the over hanging lip will break right off.
No.
However you are unclear in your description. You state there is no click at half cock, but you also state there is no noticeable click at the 'first click'. Which one is it? The first click is the so called 'safety cock' position, half cock is the second click.
Bottom line is, if you can pull the trigger and it releases the hammer from either of those two positions, the over hanging lip has probably broken off. If the over hanging lip is broken at the half cock position, put the gun down and walk away. The half cock position is the loading position, and unless the trigger is trapped and will not move it is dangerous to be loading the gun and rotating the cylinder without the trigger being trapped.
I keep calling the first click the so called 'Safety Cock' position because it is really not safe at all. Put the hammer at the first click with a live round under the hammer and drop it onto the hammer spur from a good height and the gun will probably fire. That is why you only load a revolver like this with five rounds and always keep the hammer down on an empty chamber. That notch is just too easy to break, and so is the sear.
When I examine a single action revolver with a Colt style action, if anything does not function properly I put it down and walk away.