Hello Zach,   That old caulk is “Dolphinite”.  Now just named “Dolphin” Bedding compound.  A good product.  You can get by not using bedding compound on the end of the sprit but positively use something to seal the 4 screw holes in the side, whether you use those screws or not.  (They’re not really necessary).  Unfortunately Dolphin costs about $50 a quart and you would only need about a tablespoon.    Good luck with the project.     Dave