. He plans on using his Aldi ultrasonic cleansing bath to clean these
If a DTI is similar to a clock in which a small motion at one end of the instrument (the stylus), is maginified by a gear train or rack & pinion into a large motion at the other end (the hand), then no, absolutely not. Clock gears (we call them wheels and pinions) should never be oiled. Oil in such exposed mechanisms absorbs abrasive dust and increases friction.
Cliff.