Why would I be blowing my tail lights on a 99 Buick Regal

This appears to be your answer. I googled: 2003 Buick Regal LS tail light replacement

https://www.youtube.com/watch?v=sKQkjByl4yw

How warm does it get? The computer won't turn them on unless the coolant temp gets to 235

the motor for the passenger side
blend door is shot

The actuator door on the driver's side is out of position and needs to be reset. Remove the negative battery cable for 1/2 hour to reset the computer. Start the HVAC system and you should be able to hear the door adjusting itself and cold should come out of the driver's side vent.

the light is flashing to tell u that the engione has one or more engine cylinders misfiring, have the trouble codes tested to find out which cylinder(ws) is he problem.

possible short in wiring

check the headlamp switch for a short

Hello;
On the Buick, your tail light lens are smooth with no screws accessable from the outside. So, open the trunk and you will see either cardboard or carpeted panels surroounding the trunk. Pull these away and you will see some plastic wingnuts (3-4 each side). Remove the wingnuts, and then pull the light towards the rear from the outside. Your wires and sockets will thrn be accessible. Usually depress the lock and give the socket a 1/4 turn and pull out. Replace the bulb, reinstall in the reverse order.
Hope this helps you.
Thanks;
Rich
RPM Northwest

i had one do about the same thing it also affected the headlights / dash and running lights what was found was broken wires by the passenger side trunk hinge the wires are in a flexable wire covering that runs from fender by the hinge up to the tail light lisc plate light wires were broken in there prob. from wear and tear

my tail lights on a 2002 buick regal do not go on when lights are on, I changed a couple of the bulbs still nothing, brakes lights and backup lights work.... also the inside dash lights do not work could it be a related problem,

DDennis