A mechanical gauge might fluctuate at idle or low rpm, but it shouldn't "shake". Does this only happen at low rpm? Is your gauge mounted to the engine? Does your engine have a rough idle due to a cam? An electric gauge is slow to react to the resistance changes in the sender.
If this is going to be a permanent installation, don't use compression connectors on the copper tubing. The compression ferule will cut into the copper (over time) and cause the tubing to break. Use flare fittings or a stainless braided line.
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