Where is the Turn Signal relay located on a '00 Intrigue?

It's up under the left side of the dash, attached to the same bracket as the body control module. But sometimes the problem is in the hazard switch - try pressing it when the signals don't work and that often brings them back to life. Also, check the ground wire to the left of the base of the steering column.

Most of the time with the intermittent issue it is the hazard switch that needs to be replaced. The switch is also the turn signal relay.
You can get to the switch by removing the radio and reaching behind the dash. To remove the radio there is a plastic trim around the climate controls and radio, This needs to be removed to get access to the radio screws. After removing the radio reach behind the dash to the hazard switch there are two tabs on either side of the switch, squeeze them and pull the switch out. Then disconnect the wires. Radio Remove Picture
Tools Needed: Flat and Phillips screw driver, Flash light(helpful)
The part on average cost about $120 new but I was able to find it on amazon.com for $46. AcDelco 10401280 Hazard Warning Switch Assembly