Loop - keyframe location
Location of object has to be the same on the first and last frame.
Blender doesn't play backwards, so you have to animate this backward motion.
For this simple anim ad first keyframe on start location, second on end location, third keyframe you can duplicate Shift+D from first one in timeline and just move forward in time.
Loop - Follow Path Constraint
You can animate Offset parametr - set timeline on frame 1 ad keyframe Offset with zero (hit I when cursor hovering above Offset field). Go to end frame 120 and slide Offset value until light is not in start location and hit I again.
To be precise - offset end-keyframe (light location that match with start light location) should be on +1 frame of animation end-frame.
It means that light will be on next frame on location of first-frame.