Yes, circuit breakers can go bad in that they will eventually trip at currents less than rated. That should NOT be the case with the gauge-cluster since its normal current draw is well under 5A. So even a breaker that is old and has reduced capacity should not begin to nuisance-trip with just the gauge-cluster as a load.
A key point here in your trouble shooting is that you said that the breaker would trip almost immediately. If you mean that you let it trip and then immediately reset it and it tripped again immediately, that is actually normal behavior for a good breaker. These are thermal circuit breakers and unless you let them cool down after tripping, they will trip off again almost immediately. OTOH, if you let the breaker cool down and then it tripped again almost immediately you are probably looking for a short-circuit somewhere. Examine the wiring bundle under the panel for wires that have chaffed against any of the metal structure.
As for changing the breaker, the entire breaker assembly on the right side of the cockpit may be removed from the panel as a unit. You need to remove the glare shield and then disconnect the large Amphenol connectors that bring all the wiring to the breaker module. You will also need to unbolt the heavy cables that come from battery and alternator. Once you have the breaker module removed from the panel, changing the breaker itself will be a piece of cake.
Oh, and of course you planned to disconnect the battery prior to working on the breaker module, right?