Paul, Check out page
4-52 and
4-53 in the 1948-51 Truck Shop Manual for details on the front enclosed driveshaft on your 3600. It should be the same info for your '53. I snagged a pic from my book as the picture detail is a bit better than the on-line scanned pages. That pic shows the probable leaking seal location marked by the arrow in my pic below. The rest of that section of the Shop manual describes tear-down, inspection and reassembly.
According to the 1929-57 Chevy Master parts and Accessories book
on page 477, the SEAL - RETAINER, Front Propeller Shaft Bearing for your '53 is GM# 3689176. My best guess is that seal is what is leaking, but there is probably something else worn (could be the carrier bearing) that is causing the vibration. Hope you find this helpful.
NOTE: Just some added info to what Jerry posted above
