UPDATE #1
There are couple differences between the LED module and the Halogen module that's preventing it from working.
First is the connector type. The location of the connector fins are different between two module. The halogen ones are symmetric and the left fin on led are slightly to the right. I simply cut the left fin off so it can fit in the socket.
Second problem is with the wiring of the connectors. Halogen module uses 4 pins and LED module uses 5 pins. I assume red is power black is ground. On both module purple goes to the reverse light. During the actual testing, none of the break light on the LED module lights up when applying break or using turn signals. But when I put the car in reverse the LED pack was lit up. That was because of the different location of the wiring for the connector.
I'm going to try to change the location of the wires on the LED to see if it will light up.
Below is a diagram showing differences of the connectors. Cross means that point is not used for connection.