hmm check the fuses anyway. Look on the list it has on the underside of the cover, look for "parking light, left". There's probably more than one fuse for it...
If the fuses are good (just put another one in, you never know), then maybe the bulb holder is gone or making bad contacts. There are 2 contact points on the bulb, one for the constant on, one for the flashing. BTW, a lot of people disable the constant on because that's how it is in Europe. I taped up the little knob connector on the bulb that makes it come on all the time... So a quick fix would be to just tape up th other side hehe and then both won't come on.
1998 BMW 328is - summer
1994 BMW 325i - daily
1992 BMW 325i - gone
1988 Mercedes Benz 190E 2.3-8V - sold