Right turn light and rear right tail light is out. Replaced with new bulbs and the lights still will not turn on. Please help.

Either you do not have positive 12 volts or the ground at the bulb holder. With a voltmeter or a 12v tester probe between the two connectors in the bulb holder with the bulb out and tail lights on--
If you do not get anything then probe with one lead --red in the bulb holder (switch the red voltmeter lead between the connections in the bulb holder to get a reading)and the other to a good ground --any bare metal part of vehicle.If you get a reading -that means you do not have ground at the bulb holder.
If still nothing--than it means you do not have 12v at the bulb holder. Than try finding a good 12v and work from that a reference point. Confusing? may have to have it checked out
Just in case try a bulb that you know that works..