Every year when I de-winterize I'm happy when the water pump builds up enough pressure in the system to shut off...as this means to me that no significant leaks have developed in the plumbing.
If the pump shuts off, but comes back on periodically when no one is using water then I start hunting a leak. Could be that a faucet is part way on, could be a leak under a sink or in the water heater drain plug, an outside shower that got left on, or a low point drain left open...etc.
If your water pressure is low only to the outside sink...but the pump maintains pressure in the system without running constantly I'd suspect a kinked or blocked water line somewhere near the sink. Is there a filter on the faucet in question either before the faucet or on the outlet? Does the faucet have an aerator that might be partially clogged?
If the water pump runs all the time...I'd be looking for a leak somewhere...but in that case, all the faucets would then likely have low pressure.