Here is how I do the Teak Oil. I use the Watco brand from Lowes.
I soak (submerge) the item in the teak for approximately 1 hour. I remove the item, hang, and let drip back into the pan for 30 minutes. I wipe the item dry and hang for 24 hours to dry. My shop is heated and I hang the item near or over the heat source.
I also have a drying cabinet, just a cheap wood kitchen cabinet from Lowes with a light bulb in the bottom for heat. I keep/dry my call blanks in it also.
Should you ever end up with a gummy mess the next day just re-soak the item in the teak oil for a few minutes, remove and let drip then wipe dry and rehang for 24 hrs. The teak oil soak will dissolve the mess and it can just be wiped away and re-dried. Sometimes a little teak will seep out after the first wipe down and a second wipe down may be required say 30 minutes later. That is usually the source of the sticky mess if the item is not wiped down a second time.
Hope that helps.
Fred