"It is my understanding that LED lights need a transformer. Some fixtures come with a transformer built in. Others need a transformer added on." Most of the "transformer built in" devices are using a high frequency switching power supply to reduce the size of the unit. Transformers with 120 V promaries are not small devices, witness the size of even a very low poer 'wall wart.' The volume of most of them is the actual 60 Hz transformer, and they often cannot even produce 1 amp of output current. A 10 watt, 12 volt incandescent bulb requires about 0.83 amps. LEDs are a little better (often being less than 0.10 amps each) but since there are often multiple devices present the actual operating current goes back up. LEDs often use a combination of series and parallel paths to allow for slightly higher voltages (less drop from the 120 V input) and smaller currents.

If wiggling the cord around has any effect on them, then a bad connection seems fairly obvious; you just need to work through a process of elimination to narrow down where the problem is. Try plugging the lights into the socket normally used for the MW, and see whether that makes a difference. Plug some other light fixture into the socket ordinarily used for the UC lights, and see if you can reproduce the problem. These simple tests should help you see whether the problem is with the socket or the lights. Don't imagine that the socket is fine because a MW is plugged into the other side of it; if the lights are on a switch and the MW is not, then the two halves of the outlet have been disconnected from each other and will behave independently.

The problem with using a single transformer is the high current used by low voltage lights. Concealed wiring (in walls) is also required to conform to the NEC rules for an 'approved method' and is often excessive large for individual pucks (or even a couple together) and to small for the main transformer output at high current. Pegasus Lighting should have a transformer. You need to size it based on how many watts the lights pull (and them add some margin to prevent voltage droop in the transformer). Voltage drop in the wiring to the pucks can also be an issue. Here is a link that might be useful: Pegasus Lighting

It should be easy. We have the transformer in an upper cabinet. Look at www.inspiredled.com