I had the same problem with my 95.
This is literally a 20 minute fix.
However, in step 5, where the two rows of soldered dots are, I noticed quite a bit of wear on the soldered dots, so I used a soldering gun to add some solder to the dots.
Copied from another web page:
Cluster Fix for 94-95 Impala SS &
94-96 Caprice Classic
This is only a reference, I take no responsability for this procedure. Just a guide for a fix. Use at your own risk but, it worked for me.
1) Remove the black trim around the cluster. This is held on by 2 7MM screws on the top of the trim piece. There are also 2 clips on the bottom. Remove the screws and give it a firm but gentle pull towards the wheel.
2) Now you will see 4 black 7MM screws holding the cluster in the dash and 8 silver T-10 Torx screws holding the cluster together. First turn the key to the off position, not the lock position, and put the gear selector in Low 1.
3) Loosen the cluster by removing the 4 black screws and pull the cluster towards you. There are no other cables or clips holding it in. There are only two plugs in the dash that it plugs into. Just be careful not to break the shift indicator cable that is on the cluster. You can't buy just this piece from GM.
4) Now here is where you should take your time and be sure to pay attention to how this comes apart. (In other words, send everyone else to do something and leave you alone) Take out the 8 Silver Torx screws and put them aside. Now the whole front of the cluster is loose. Take off the clear cover, then the large black trim behind that, then the thin black piece, and the shift indicator with the green window. The indicator with the window you will have to put aside but remember BE CAREFUL of the cable.
5) Now you will see the display in front of you. There are 4 RED TORX screws holding this to the cluster. Remove these screws but be careful because these are the only things holding this display to the cluster. There are no other wires or nothing. This is the problem. When you take this out, you will see two rows of soldered dots on the display, one on top and one on the bottom. Clean these with contact cleaner or alcohol. You will also see two black towers with little spring loaded tabs in the cluster. Clean these with alcohol also. I had two that were stuck down so I pulled them up very carefully and put a bit more tension on them and all the others.
6) Now just reverse the procedure I gave you here and you should be in business. Just be careful of the Temp. Gauge needle when you put the thin black trim piece back in place. What I did was put the cluster back together and then just push it back into place and tried it before I put all the trim back.
This sounds a lot harder then it really is. Once you get into it it's not that bad. If you don't feel comfortable doing this, let a friend that has taken a dash apart before help you. You just have to go slow and don't do it when you are in a hurry. This whole thing should take about an hour or a little more. If you are not clear with any of the steps above, let me know and I'll try to clarify it a bit more for you.
Good Luck