I have a 1995 Blazer that only has the daytime running light and highbeams, when the truck starts the green indicator for the DRL is on when I switch the lights on they go out I flip the high beams on and I have high beams I have check the relay in the glove ox and swapped it with another and no change, it just seem strange that both lamps are burnt out at the same time

Make sure the headlight bulbs are good.
And getting 12 volts and ground to them.
Sometimnes the burn out witin 10-15 minutes of each other.
Kinda like a built in timer!!!

Check all fuses.
MT