Welcome Harperjones to the HDTimeline forum. You will find plenty of fellow riders and enthusiasts eager to help you do maintenance and service on your ride. Take a look at the Self Help and Search tabs near the top of this webpage to help you work your way through.
That said, since your bike is an '03...I would probably look at the actual switch contact going bad or having a problem with contacts/corrosion as the controls and switches are subject to weather and riding conditions, especially if you recently did a "through cleaning" (technically no water spray above the side covers is what I would recommend, but JMHO). The switch gear access is fairly straight forward, you will need good set of Torx bits and screwdrivers, but you had best get a service manual to reherse your routine and do it on a Friday to be sure to get you two full days, just in case you have to go to the dealer for parts. You also have to be careful about small parts and springs falling out, so go slow and careful, inspect everything before disassembling ANYTHING.