(1 hour or less)
You can make a two-way mirror from inexpensive Mylar™ reflecting film and ordinary window glass. The variable illumination is accomplished with dimmers commonly available at hardware stores.
To make a two-way mirror, put the reflecting film on one side of the glass, following the instructions for the particular brand of film used. Cover the edges of the glass with cloth tape to prevent the film from peeling and to avoid cuts from any sharp edges on the glass.
Place the lamps as shown in the diagram. Connect each lamp to a dimmer switch and an extension cord.
Stand the mirror on a table. This may be done by standing the mirror between two heavy masses (such as 2 pound [1 kg] lab masses), or by making a wooden stand of some sort. A "sandwich" of two pieces of wood with the mirror in the middle, all rubber-banded together, will work. If you have a table saw, cut a slot for the mirror in a piece of wood. Anything that works will do.
(15 minutes or more)
Sit across the table from your partner with the two-way mirror in between. The room should be dimly lit or dark. Be sure that you and your partner are the same distance from the mirror. You should be able to see both your partner's face through the mirror and your own face reflected in the mirror. Line up your reflected eyes and nose so that they coincide with your partner's. You will have to adjust your distance from the mirror as you do this. Point one lamp directly at your face and have your partner point the other lamp directly at his or her face. Adjust both lamps so they are initially very dim. Now use the dimmer to vary the amount of light reaching your face. Have your partner adjust his or her dimmer. Watch your features blend with your partner's features.
The mirror reflects about half of the light that hits it and transmits the other half. If your lamp is dim, there's not much light to bounce off your face and reach the two-way mirror, and your reflection will be dim. If your lamp is dim at the same time your partner's is brightly illuminated, then light from him or her will be transmitted through the two-way mirror and you will see his or her features clearly. As you make your lamp brighter and your partner makes his or her lamp dimmer, you will see more of your own features and less of your partner's. Your brain combines the two images into one perceived face.