While looking for the switch do not restrict search to W113, under the link provided you have W109 and W114 as well. Sometimes the same part for W113 costs much more than for other "W".
The lamp is A 100 820 01 62 and it is called License Plate lamp. I understand you have it.
The pad for switch is H 10 120 825 00 96 (may function as A 120 825 00 96). Used in 108, 109, 110, 111, 114 and 115.
The switch is A 000 821 02 52, this is the one with two screws, used in 100,105,109,110,111,112,114,115,120,121,123,128,180,186,188,189,198,309 and 310.
However, the shape of the hole in your trunk suggests that you had there a regular door contact switch, A 0008211552, which is normally available at Mercedes ($70) and many other places, used in 100,107,108,109,110,111,113,114,115 and 123. This is what I would go for, looks like this:
https://www.niemoeller.de/en/w111/w111-mercedes-benz-220sb/B012/820102/d82218-door-contact-switch~2