PIR triggers relay without motion
The PIR needs a clean Vcc and no switched bright lights near the sensor.

I don't know how much a glitch your Rleay causes on 12V nor the proximity of the LEDs near the sensor.

Here's your datasheet. https://components101.com/sites/default/files/component_datasheet/HC%20SR501%20PIR%20Sensor%20Datasheet.pdf