Whatever that is (the plastic used for the needles) - it is one of the few materials that superglue actually sticks to.
Try just the tiniest drop on one side of the break and hold in place for a minute.
Some more dash/instrument panel restoration tips:
Also it might be good to note that a common failure point is at the interface of the PC board and the wiring harness - where the 18 conductor clip stabs in to the back. If you are doing a restoration and still need to drive (with gauges & speedometer) it will definitely come out - alot. Just a few times plugging in and out can leave that area of the pc board pretty well torn up.
I learned early on to release that wiring group (the gauge feeds, power, grounds, directionals, etc) from the main artery of the under dash harness. You only get an extra 6-8 inches of slack but that comes in handy when doing a cluster pull. Another trick (speedometer cable) is to pull as much slack as is available from under the cab and push it through the firewall.
Doing those two things allows the cluster to be pulled in towards the steering wheel and then the wiring harness can be released and speedometer cable unclipped without digging around in back of the dash.
If you have a 4WD indicator or check engine light that mounts out side the main gauge board (usually up top) it helps to splice in an extra 10-12 inches of wire. The factory wires are short and the added wire allows you to twist the lamps in with the cluster resting on the steering column.
And, as I discovered from a bad experience, the white scale markings and letters on the dial faces will smear easily. If the faces are dusty, resist the temptation to use any thing other than a mild soap and luke warm water solution to clean them. Even then, don't rub them with anything - a finger tip can smear the white paint and make the face look like crap. Only swish the gauge around in the soapy water and rinse clean. They will come out looking brand new. If you have to get a stubborn layer of grime off, use a q-tip to cut in around the markings.
For some reason the orange paint on the rays is much more stable - it never seems to run.
If you do smear some white markings a tiny bit of WD-40 on a q-tip will remove the white and not disturb the satin black background.
When reassembling the gauges, lens and bezel to the cluster case apply a bit of vaseline to the T-2 & T-4 screws. It really reduces the amount of cracks in the screw holes. And do not overtighten them - they will never back out.
The shadow plate that goes over the gauges and under the lens takes flat trim black paint real well (duplicolor or Sem). and makes the whole job look sharp.
If the plastic lens is not too badly scratched try Meguiars PlastX. It really does work - put some on a buffing pad and strap it to an orbital sander. Do it while you watch TV one night. - it can't smooth out deep scratches but normal hazing caused by years or wiping the dash with paper towels will go away.
Having said all that; I have plenty of dash stuff laying around. If you still need a needle (or a gauge), send me a PM.
