I would think this Pontiac will do just fine towing - back in 'their' day, this vehicle was considered one of the great towing vehicles (389/421 with the turbo400 trans!!) along with the "full sized" Oldsmobile/Buick/Cadillac/Chrysler/Dodge/Ford and 'big block' Chevs. Back than, PU's really had not yet hit the 'towing vehicle mark' yet as they have now-days with all of the power options they offer today. There were no extended cabs/multi-door'ed one's available yet and it wasn't till the mid-seventies that they even started offering the big motor power-train's that were already in full sized cars. The '65 Catalina SW my dad had always did just fine when towing - the one thing I would check into doing (if not already done) is the up-dating of the brake system to a newer front disc/dual master cyl system - I would think the 69/newer disc set-up would probably be adaptable to this 65.
The front brake hose 'breaking' incident in 1969 when I was 15 and backing the boat trailer into the water comes to mind. I backed it in stopping when he told me to, thus holding my foot on the brake pedal (still in reverse-like I said, I was 15

) a front brake breaks - brake pedal goes to the floor, I slammed it into drive pulling forward out of the water as I get it stopped with the e-brake - I than find him drenched and in the water holding onto the boat. '65's (everything made than) still had just the single cylinder brake systems and if any part of the system failed - you lost it "all" of the system!! It wasn't till '67 when they changed over to the duel cylinder setup and about '69/'70 when front disc's started being offered (as a option-extra $$).