If nothing else, Mysterious Marfa Lights Viewing Center is in a beautiful location with a lot of great information on the associated markers about the mountain ranges, geology, and plant/animal life in the surrounding Chihuahuan Dessert- So get there early, before sunset, take a walk around the trails, and take in all the sights.
All that being said: The lights you can see every night, to the Southwest (right, from the viewing center), moving over and to the right of the flashing red microwave transmitter tower, ARE NOT the mysterious Marfa Lights (the info center even tells you this, but most people don't bother to look at it). While it is fun to watch them and marvel at the remarkable clear-air visibility at this altitude, if you are looking southwest, you are looking at headlights on cars heading into Marfa from the south on Hwy. 67.
The REAL Mystery Lights can be seen (and only on about 15 or 20 days out of the year, I might add) against the rising terrain to the southeast. If you look SE (left) and see the small mercury vapor light off in the distance, you'll want to focus your attention between it and the red flashing tower. This is where the Mysterious Lights can be seen, if they appear.
The locals and people who have seen the real thing say that the lights are generally reddish and tend to dance among and around each other, often heading off in tandem or in odd directions. I've heard one eyewitness account of a light that nearly buzzed the center itself before silently dissolving into hundreds of little individual lights.
I managed to see one non-headlight out to the southeast on one out of three nights. It was reddish, and maybe half of the distance between the Viewing Center and the moutains. It flickered and transited from west to east for only about 15 seconds. The people looking southwest at the headlights on 67 completely missed it, unfortunately.
I don't know what they are, but something is out there.