Hardway

I had this same problem with '88 300zx with an all digital cluster. The cluster should have a control box/computer under the dash. Make sure it is properly secured to its mounting location, check for wires/plugs going in to it, and if it possible to unplug it clean all the contacts. It sounds like you have a ground/connectivity problem since the cluster does light up sometimes.

How did you end up bridging the oil lines? Did you have to make something or were you able to buy something off the shelf at a parts store?