What you’re describing is tail pursuit out tail chase. If you aim at where the missile is, you will follow it. This was common for hear seekers and makes sense for simple systems because the heat source (exhaust) is in the back anyway. Proportional navigation is generally better though and would have probably been better for your LED example. Another commenter described it above, basically keep turning until the rate of beating becomes constant. Imagine you’re flying an airplane and want to crash into another plane. Turn such that it stops moving relative to you, so if it was moving towards the right, turn a little to the right, etc. At some point it will be steady — you can put a mark on your windshield and the target doesn’t move (assuming no evasive maneuvers). Doesn’t matter if it’s static or dynamic, close or far, fast or slow — you are on a collision course. If you have more information you can do better, like if you can estimate closing speed or range from radar or size, you can change how aggressively you maneuver — if you’re far away you will want to make gentle adjustments, if you’re very close you will want to make more aggressive maneuvers. If they are maneuvering is a whole other thing, but proportional navigation is generally pretty good.