do NOT allow the oil to pool on your paint.
do NOT use silicon lubricant = WD40 and such, they will wash out in the first light rain and can damage your paint.
The normal binding point is in the pivot pin on most post WW2 cars.
The problem is the pivot pin corroding, getting packed with sediment or drying out and binding.
A careful application of lubricant can bring them back to proper speed and function.
The difficult part is; you must "saturate" the pivot pin that the wiper arm attaches to with automatic transmission fluid, while the wipers are running.
#1. Remove the wiper arms.
#2. Take eight or ten paper towels, cut a hole too fit the pivot pin in them, and put two or three over each pivot pin too protect your paint, you may need to stop and change them several times.
#3. Wrap cotton or gauze around the pivot pin and wrap that with tape.
#4. Soak the cotton with fresh transmission fluid, using an eyedropper, until it starts to run down the shaft.
#5. Start the engine, turn the wipers on high and let them run for fifteen minutes, adding fresh transmission fluid as needed.
Total fluid volume needed is roughly one ounce for both pivot pins.
You are creating a saturated wick = controlled leak.
The movement of the pivot pin will draw from the wick = rough total penetration ten drops per pin.
Not enough to be a concern of leaking into the car.
If you see the pin speed up, the run time can be reduced to fifteen minutes total.
You may repeat this as often as needed.
This procedure requires patience and care.