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That is probably the start solenoid and it is clicking for one of two reasons. The contacts may be burned and it may need replacing OR the more probable cause is that the battery is either low on charge or needs replacing due to the fact it can't supply the needed amperage. Gauges take almost no power at all and so a little surface voltage can do that. I would start by taking the battery out and into a place that sells them for testing. It may just need a good charging or if bad, it can be replaced. Hope this proves helpful here. Please get back to me if we need to dig deeper into this once you have eliminated the battery as a proximate cause.
The contacts and the battery leads may be dirty and just need cleaning. Always something to watch.
Just checking back in to see if you were able to resolve this issue or do you still need some additional input from me?