I agree with the following:

Changing seatposts including the captain's are cheap and save quite a bit of weight for little money.

Wheels have been mentioned would improve the ride and would save a lot of weight. Not cheap but worth the money.

Depending on where and how you ride ,ou may want to keep the disk brake but it does weigh a lot and taking it off is free. Might be a possibility after you get the rim brakes sorted out.

Fork has been covered - might be able to save half pound but high cost per gram.

Cranks - Cranks and BBs of that era are pretty heavy. Davinci cranks would save quite a bit of weight or you could spring for Lighting cranks but that is really a lot of money.

Doing everything I think close to 30 lbs is achievable but that would only save about 5 pounds. Sounds like a lot but keep in mind it is really for with two people and two bikes.

I suggest:

1st - Getting the brakes functioning well is the first priority. Keep in mind you can grab the rear brake as hard as the front on a tandem.

2nd - New wheels will improve ride as well as drop weight. Either TX2s or slightly heavier conventional 36 or 32 spoke wheel set that would weigh about 2,000 grams.

3rd - Ride lots. Put 5,000 miles on it . Make sure your stoker has bought in and decide what type of riding you want to do on the tandem. You may want to race, day ride or even tour who knows riding together is different.

4th - With that experience on a tandem you are in a better position to decide if you want to upgrade that aluminum frame to get a really good 30 lb tandem or spring for a $10,000+ carbon bike depending on how your riding and finances are working out. Who knows after that time you might want a time trial bike, or a bike with couplers to fly with, or a bike that can handle panniers.