H i at this point I would say you have a short in the electrical system and you will have to do some testing you wil need a 12 volt test light so you will be able to check some electrical circuits the first thing I, would check is all the door jams to make sure that all the door switches are working ok if all door switches are working ok I, would remove the head light switch this is where the power comes from for your dom lights, some times these wires that go to the head light switch get hot and they melt together and create a short check to make sure this is not your problem if this head light switch has been hot replace it and see if this takes care of the proublem of the dome lights staying on all the time as far as the back up lights go you need to look up under the truck and make sure the wires running from the trsnsmission are not shorted and staying hot all the time.I, hope this helps you if you need more help please get back with me Thanks,

Al

you need to pick you up a hays repair manual if you dont have one so you can trace these wires.