Bright Object in Sky NNE of Deming, NM

I reside in the desert about 5 miles east of Deming and 5 to 6 miles north of the Florida Mountains. I went to my backyard to see if Jupiter was still visible. My wife and I watched it for three nights and saw it earlier this evening. When I looked in the sky NNE of my backyard, I noted a bright, star-like object that appeared to be pulsating from a bright white to bright blue. While I watched, it appeared to move right, then left, up and down and left and right again. Sometimes it would go right then left to its original position. Sometimes it would go right then left back to the original position. I called my wife outside to see it. We looked at it though binoculars. When viewed through binoculars, the object appeared to have a tail due to movement of the binoculars. When I steadied it on a solid dumpster, the object was clearly visible and much brighter than the surrounding stars. The pulsating bright blue lights were visible with the naked eye but were clearer with the binoculars. We watched for about 30 minutes then I came inside to make this report.