The easiest thing to check is the GFCI plug and breaker. It is SO important to be sure that the GFCI feature on the plug associated with the pool light is working as designed. It is designed to cut the power when it senses a fault or electrical failure. We have also found that at times, depending on placement of the plug, they can trip from outside influences. Check those first.
When we find out that a bulb is bad, we will always replace the gasket during the bulb replacement.
Switches and relays are for the most part, a relatively common repair. There have been times that these types of repairs can be caused by a separate issue that must be dealt with for safe pool light operation.
Water and the inside of light fixtures are a bad combination. This will usually lead to complete replacement of the fixture and wiring. Generally speaking, the older the fixture, the larger chance of a leak from the gasket. Water can also enter the fixture from the sealed area where the wire enters the back or side. We feel that once water has been inside the fixture, it should be replaced for safety reasons.
There are now white, as well as color changing LED pool lights.