Guess what I've just done to my JMJ mustang?
I use Dunlop 65 but other brands specifically for instruments are available. Never use pure lemon oil, or anything labeled 'lemon oil' which is intended to be used on furniture.
Two squirts on a piece of kitchen towel is enough for the whole fingerboard - and practially all of that is then wiped off. Once a year is more than enough - I probably do this to each of my basses/guitars/ukes less than once in every five years.