While smoking a cigar in backyard, noticed a pulsating, star-like white, amber light very low on the horizon to the south, stationary at first, then wavering and hovering east, west, ascending, descending and ultimately very slowly descending below tree tops not to be seen ascending again. The movements and ultimate descent out of sight took a full five minutes. No strobe or beacon lights seen, but object appeared to be at least three or four miles away, possibly more. There was no helicopter or aircraft noise. Sighting was in vicinity of U.S.-Mexico border; possible that object was actually physically positioned over northeastern Mexico.