@Pᴀᴜʟsᴛᴇʀ2's answer is excellent. But, I'd like to add: rather than just twist & tape, there's something called a "lineman's splice," or "Western Union splice" which provides a great electrical connection as well mechanical strength, and is easy to do. (see Wikipedia's illustrations., or google "lineman splice" or "Western Union" splice - there are a few good videos on Youtube.)
The technique gets its name from its use in repairing telegraph and phone wires. If it was strong enough for wires out in the elements, strung between poles over many miles, it's probably strong enough for your instrument cluster.
In my experience, this holds up better than twist caps, and you won't wind up with the situation where you've twisted the cap on, and the wire breaks or one of them is miraculously not secured inside the cap. And, this doesn't require any special hardware.
This is more common with solid-core wire than stranded, but it works just as well for stranded wire.
( from Wikipedia)
The idea is:
- Strip about an inch of insulation from the end of each wire.
- Slip a 1" piece of heat shrink tubing over one of the wires. Do this BEFORE connecting the wires to each other as it'll be impossible later.
- Bend the wires at 90 degrees half way between the end of the insulation and the end of the wire.
- Hook one 90 degree bend over the other, so that the wires are colinear, but the bent parts point in opposite directions.
- Twist the protruding bit of each wire so that it winds around the other wire.
- Tug the wires in opposite directions to tighten the joint
- Solder if you want to- I would - but it's not strictly necessary.
- Slide the heat shrink up over the exposed wire, hit it with your lighter or heat gun, and call it a day.
Shouldn't take more than about 10 minutes per wire. If done properly, it'll last longer than the car.
If you don't have heat shrink lying around, you can get it from your local auto parts store for cheap. You could use electrical tape, but I despise electrical tape. It's sticky, melts easy, and just screams "amateur hour."