It sounds to me that you have a bad engine ground, and the system is somehow only getting adequate ground through the clutch and transmission.
Use a volt-ohm meter and check the resistance between the battery negative and the following points:
- engine block
- alternator body
All should be zero. If not, find out why. Remove and clean the ground wire connections. Use new lock or serrated washers on bolted connections and wire brush the area to get a paint-free connection. A ground to sheet metal is best when you have a rust-free self-threading screw into a new hole. In an old connection, sometimes you have to drill a slightly larger hole and use the next size screw. For threaded holes, wire brush the bolt and hole to get a clean connection.
After you get the grounds connected permanently then you can paint over them. I like to use CRC marine heavy duty corrosion inhibitor to protect these small areas.
I have a FAST EFI system, and like all of the modern electronics, they need good grounds. On my car, just below the battery, I ended up with an ugly stack of ground connections to the factory chassis ground location, so I installed a marine-grade grounding bus to connect all of the grounds that these systems need. (Bluesea.com, available through Amazon.) I have a #10 wire from this bar to the heads, since I wasn't getting zero resistance between the block and heads.