Replacing broken tail lights

Have you tried going into the trunk and removing the panels covering the lights inside?
Hope this helps.

if the panel is not damaged or only slightly damaged it should just be a case of removing the damaged tail light and fitting the new one, if all electrics work I would leave the socket

Open hatch, remove the 2 screws on the side of the broken light, pull firmly and replace.

to replace the GM tail light bulb, you will drop down the tail gate and you will notice 2 screws on the tail light assembly, you will remove those 2 screws with the proper screw driver, once you do that the whole tail light assembly will come off, then you will see onother 2 screws holding the light panel to the tail light assembly, or brackets holding the light panel to the tail light assembly remove either or and you will have access to the three bulbs on that light panel, replace the burnt one and follow the same intrunctions to put back.

Yes, you have to remove the plastic panel. It is mostly held by spring clips. You can see how to remove it at the link below.
http://www.odyclub.com/forums/52-2005-2010-odyssey/52868-can-t-open-liftgate.html

tail light bulb broken/out remove backside nuts and remove lens and replace as needed
taillight lens broken same thing remove backside nuts and replace ..for affordability try a salvage yard
as a temporary fix red or yellow electrical tape ...i hope one of them was an answer to this question as i dont have much to go on ...

and Repair Notes TAIL LAMP REPLACEMENT REMOVAL PROCEDURE Open the rear compartment. Remove wingnut and pull back the rear compartment trim panel from the tail lamp. Remove the wingnuts from the tail lamp. Remove the tail lamp from the rear body panel. Disconnect the electrical connector from the tail lamp. Remove the tail lamp socket, turning counterclockwise. Remove the bulb from the tail lamp socket. Remove the sidemarker lamp socket, turning counterclockwise. Remove the bulb from the sidemarker lamp socket. INSTALLATION PROCEDURE Install the bulb to the tail lamp socket. Install the bulb to the sidemarker lamp socket. Install the sidemarker lamp socket, turning clockwise. Install the tail lamp socket, turning clockwise. Connect the electrical connector to the tail lamp. Install the tail lamp to the rear body panel. Install the wingnuts to the tail lamp. Pull back the rear compartment trim panel to the tail lamp and install the wingnut. Close the rear compartment.

Most cars tail lights are atached by a couple of nuts from inside the trunk. you will have to peel back the carpet , or remove plastic cover panel if there is one.

Open the trunk and on the inside panel (usually grey with a carpet texture) you will find black knobs with hooks on them for a cargo net to attach. unscrew all of them and remove the panel. You will find studs from the tail light sticking through with sheet metal nust or plastic nuts. unscrew them also (usually 4 to 5 nuts). now pull out on the tail light and squeeze the light sockets and twist counter clockwise and pull the socket and bulb out. Replace the tail light with a new or good used one and reassemble everything in reverse order.