Cut a notch equal to the width of the body of the LED light along one edge of the plexiglass.
Grind away the majority of the outer glass of the LED bulb. Use caution so that you do not nick any of the conducting elements inside the diode.
Slide the LED into the notch on the plexiglass. Secure the light by wrapping the notched edge with aluminum roof flashing tape. Ensure the tape is not touching any of the electrical conductors at the base of the light.
Continue wrapping around the edge of the plexiglass, covering the front and back edge of the notched side with tape. One pass is sufficient.
Connect the two legs of the LED to the controlling device. Consult the instruction manual of the controlling device for specific connection methods.