It's really hard to get pictures in this area while holding the meter, alligator clip is on its way tomorrow to make this easier. Should've ordered one to start with.
If I am looking at it right and what you describe is correct the pool light will only work when the spa switch is on.
Spa light works regardless. Pics uploading
36 volts on that side when the switch is off means bad switch.
That switch is 3 days old
It is still a 3 day old bad switch. The circuit should be OPEN and you would get no voltage on the terminal you are testing. Have you removed the light(s) from the socket(s) before testing?
Wouldn't be the first time a junk switch caused problems. For starters, your black probe should go to ground and the red should be used to check for voltage. Having voltage on the fixture side (the red wire goes to the light, I assume) means either you are getting something coming through the switch. (bad points, crud, random crap) or you are getting some voltage coming from the neutral side (white wires), or third option, you are getting some sort of stray voltage from another source (another unknown short). Start with pulling the wires off of the switch and remeasuring each side. If you get 120 on the hot and 0 on the fixture side, then its the switch. If you are still getting 36v on the fixture side, you have one of the other problems.