I have a 98 Olds Intrigue. Hazards & Blinkers flash in the rear only.... the front lights up solid, no blinking. When disconnected from the head lamp assembly we have tested the flasher wire....

Is the bulbs burned out? That causes the rear to flash fast did one go out then the other or at the same time? Sounds like bad front bulbs. If not check the connector.

The blinkers work through a flasher relay. This might have failed. Try turning on the hazard flashers to see if they blink. If they don't flash it is probably the relay at fault. Please note some Buick models use separate relays for the blinkers and the hazard lights. If the hazards work and the blinkers don't you've got a 2 relay version. Sparky Answers Changing The Flasher On 2003 Buick Century

check the ground wires to the rear lights sometimes the head lights will provide backfeed ground when off but cannot when on this would explain the rapid flash

Check the switch

If both front & rear lights light up but dont flash the turn signal flasher is bad. Verify all bulbs are lit, on both sides of vehicle front & rear.

Sounds like the signal multi-function switch has a short it it. Get a new one.

check for open grounds to the rear lights

Possible cause is the connector is disconnected and the bumper area. Main ground wire may be loose, check manual for ground location. Also the wiring loom may have been damaged between the rear lights and the front connector. The front lights will blink fast when the rear lights do not work. There could also be a problem with the turn signal switch. Check with the wiring schematics to see which wires to check for power.

DT

try some electric contact lube in the light socket the leads may be corroded