Are you talking about this?:
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If so. that isn't a ground, it's a fiber optic cable. It diverts a bit of light from the lamp in the upper RH corner of the cluster and use it to illuminate the ashtray:
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Your cluster wiring has two connections to ground. While looking at the male plug (i.e. the harness side) with the larger locating tab on the bottom, the ground wire pins are:
With no gauges - the lowest one on the left and the 4th from the top on the right.
With gauges - lowest one on the right and 3rd from the top on the left.
Both of these ground pins are lead to a common splice point. That splice point has one lead which is connected to the ground bus block - located on the side wall above the e-brake actuating mechanism.
Is it just the cluster lighting that is out - or are the gauges (if you have gauges) out as well? If no gauges, do the warning lights/gas gauge work? If everything else is working, that would pretty much eliminate a ground issue because all the components on the PC board share the same two grounds.
Look at the hot side instead of the ground side;
The instrumentation lighting is fed from the H/L switch on the DK GRN 44 lead. The DK GRN 44 lead feeds the line (inlet) side of the INST LPS fuse. I am sure you've checked that fuse - and with a meter - right? The load side of the fuse is connected to the GRY 8 lead which goes directly to the cluster plug. It terminates at the 2nd pin from the top on the LH side (looking at the male plug) - that is with or without gauges.
You will have to use a meter - or test light - to trace the circuit and see where the power is being lost. Do these checks with the dimmer rheostat turned all the way up:
Pull the INST LPS fuse and check for power on the line side (should be the RH side looking fwd). If there is power there, that would confirm that the DK GRN 44 lead from the H/L switch is good and power is available to the fuse. If not, check the other end of the DK GRN - at the H/L switch and confirm power there. Power at the H/L switch and not at the fuse means a broken DK GRN lead.
If power is coming into the fuse, the next check is for power (on the pin connected to the GRY 8 lead) at the male side of the cluster harness connector.
That should get you started.