Sounds like it may be the fuse. If it's good, then you might pull the tail light lens and a bulb, then check with a multitester to see if your running light circuit is getting power (there are two + contacts @ the socket base--check 'em both, as only one will have power to it w/o the brake applied). The bulbs are dual filament, and the running lights (5w) are on a separate circuit from the brake lights (21w). It's highly unlikely that you would lose BOTH running light filaments in both bulbs, while retaining the brake light filaments. FWIW, federal regulations prohibit the use of amber running lights from the rear of a vehicle, so no, the turns won't be lit unless you're signalling a turn. Let us know what you find....
Never try and teach a pig to sing: it's a waste of time, and it annoys the pig.
--Robert A. Heinlein