There is nothing odd here with a 1965 Caravel
not having a grey tank - they did not become standard until '73-'74. All trailers before then let grey run on the ground - it was normal. If you are at a full-hookup campground, the grey runs into the sewer connection - no problem.
Today, grey on the ground is okay in some places, but not others. In places where it isn't most people use a blue tote to capture grey water and dispose of it in an acceptable manner.
Adding a grey tank is not necessary if a blue tote is used...keep in mind "grey water" is just wash water from the kitchen sink and shower - not your toilet. We use a tote when not hooked-up or in an area where grey on the ground is not allowed, it really isn't a big deal - but you have to decide that on your own.
The issues to deal with when adding a grey tank include:
1) finding the room for it inside the frame so it isn't hanging down too low
2) dealing with the added weight of a full tank - may take away for inside "stuff" you can carry
3) plumbing it in to capture your grey water without impeeding the flow of your black tank
4) added stress on an already light-weight axle/spindle - if yours hasn't been changed yet, I definately would if you are adding a grey tank (do a search on "1965 Caravel spindle or axle")
Each era and model is slightly different with their connections and fittings - so you really need to understand how yours work before you get into it. It can be done, but it is not just a simple bolt on installation without some ramifications.
Good luck in whatever you decide to do ~