Before proceeding, be sure the LED flasher is well grounded...
The purple wire feeds voltage from the flasher unit to the turn signal switch for only the turn signals.. I've never installed LEDs on one of these old vehicles, so I'm not sure if the LED flasher unit is normally closed (N.C.) or not.. The stock flasher is N.C... This means that whenever the ignition is on, the purple wire is hot even if the turn signal switch is in the off position.. IF the LED flasher unit is normally open (N.O.), the purple wire will not be hot until a load is applied -- the turn signal is activated..
It sounds like you could have a bad flasher or open circuit (broken wire).. To check this, install the stock flasher and disconnect the "horse shoe" connector.. Turn on the ignition and check for voltage on the purple wire on the body harness side of the connector.. If you have voltage, the wiring is good, the LED flasher is bad...
{EDIT} LEDs are polarity sensitive.. You may need on of these:
https://www.classicindustries.com/pr...ts/f90652.html