Getting the turn signals to work
Most cars use a “flasher” plugged into the turn signal fuse box that opens/closes the circuit which causes the turn signal lights to flash.
“The reason most mechanical flashers won’t work with LEDs is that they require very little current flow, which is not enough to heat the internal strip and open the circuit” – MotorTrend
You have to use an electronic flasher that is made to work with LEDs. The Tempest uses reverse polarity (rare?) so I ultimately ended up using this one…
United Pacific 90652 LED Flasher w/Polarity Reversing Adapter
Getting the turn signal indicator to work
Most vehicles have a separate right and left turn signal indicator on the dash. The 1964 Pontiac Tempest only has one, which presents a problem when LEDs are used on the exterior turn signal lights. Instead of indicator blinking along with the exterior lights, it just stays on solid.
This has to do with LEDs being dual polarity. To fix this, you need to install a diode that prevents power coming from the right or left light from energizing the other light. On the image below, the red wires connect to the right and left lights and the blue wire connects to the turn signal light.