All of the the instrument lights including a factory tach use the same fuse.
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The parking light fuse is often shared with other circuits, but since its the instrument fuse (probbaly 3 amp in '71) then its downstream of the fuse.
If the bulbs are not burned out then I would follow the orange wires looking for locations any one of them could rub or chafe against sheet metal.
The diagram in the '71 shop manual
may show the junctions for the the instrument lamp feed (orange wire).
I've found on my 67 the orange wire goes from the fuse box to the steering column connector where it is spliced to another orange wire. That second wire then has a welded junction in it buried in the harness. One wire goes to the console, another to one side of the instrument cluster, and the last to the other side of the instrument cluster. If you see two orange wires at the column connector, that's an easy place to disconnect and test for shorts to ground. That's just an example of how to narrow down the problem location.
