A new variation of the drop-off method for fabricating field emission points by electrochemically etching tungsten rods in a NaOH solution is described. The results of studies in which the etching current and the molarity of the NaOH solution used in the etching process were varied are presented. The investigation of the geometry of the tips, by imaging them with a scanning electron microscope, and by operating them in field emission mode is also described. The field emission tips produced are intended to be used as an electron beam source for ion production via electron impact ionization of background gas or vapor in Penning trap mass spectrometry applications.