I would consider light oil to be anything other then gear oil. Any motor oil in the 0 to 40 weight range including straight 30 will work. One quart of 5W20 would last a long time for light oil lubricant.
I notice when changing oil in my mowers, the straight 30 weight is stringy and sticky where as the 10-30 poured right in. This could be a plus if you want the oil to cling to the shaft better. Straight Lucas oil additive would be a great lubricant for slow turning shafts, this stuff clings and strings to everything. I bought 30 weight oil for lawn mowers at my local ACE hardware for a fairly cheap price.