ir proximity sensor circuit
I suspect that this is a sensor for detecting body heat. The TSOP1738 is used for remote control operations, I believe. Since there is no concentrated IR source to detect, I wonder if the TSOP device would be useful.
These simple detectors are really just monitoring the entire heat distribution of the area they can see. They react to changing IR patterns.
The front end portion of the X10 motion detector is a similar circuit using a dual opamp. See the link below for the schematic.
https://www.edcheung.com/automa/ms14a.htm
The problem with the simple circuits is that after a short time, the hot body gets averaged into the background thermal profile. (If the circuit cannot track the background profile, then you get lots of false triggers due to temperature changes or sunlight heating up objects.)
Therefore, it is not easy to detect someone standing in front of the sensor for a very long time. Instead, you have to detect only the abrupt changes. When the body heat IR increases rapidly, you assume the person is present and turn on the LED. When the body heat IR decreases rapidly, you assume the person walked away and turn off the LED.
Since the X10 devices are inexpensive, I would suggest getting one of those to play with and modify. I would suggest that you will have to replace U1 with a micrcontroller that does the timings you want.