Start by ensuring that your battery is charged as it can easily muster the current to click relays yet still not have enough to instigate the trim pump.
I would start by probing with a test light the large blue UP wire going to the pump or the large green DOWN wire.
Connect the test light clip to the battery's negative terminal stud, touch the test light probe to the positive stud to check the bulb and then probe one of the wires while simultaneously throwing the trim switch in the direction that corresponds.
If it lights up your problem is in the pump or is with the pump ground.
If it is a brush contact issue in the pump, simply rapping on it near the top where the wires go in with a rubber hammer, while activating the switch may be enough to get it spinning.
You might want to look inside.
This link should provide you with the help you need.
Troubleshooting Mercruiser Trim Pump
This link addresses a different problem but explains the wiring fairly well too.
More Troubleshooting.
Good Luck.