Serial Data through Pin 13 LED
If you are going to use an external LED, then using software to make the LED blink when the RX or TX line is busy is a waste of your CPU. 

Instead, simply connect the LED to the RX or TX line using a transistor as a buffer to prevent the current draw from messing with the serial signal.

To borrow an image from this answer to a similar question:



You can try omitting the transistor buffer, but the serial waveform will be altered, possibly to the point where data becomes corrupted. The transistor prevents the current draw of the LED and resistor from loading down the RX or TX lines.