Congrats on the new to you boat!
Given the age of the boat, I'd start with hoses and clamps. Hoses have date codes on them. Are they original and marine grade, and designed for fresh water use? It may be time to consider replacing fuel hoses, fresh water hoses, sink /shower drain hoses, sewer hoses if that has not been done. That's a good time to look at hose clamps and other associated fittings.
Are the tank vents working? Even if partially clogged, it can cause the tank to become pressurized / create a vacuum which can then cause leaks as it damages seals.
Start with a an empty tank. Have someone on deck fill them. Look for leaks. If you're not sure, place paper towels in key areas and keep an eye on them as the tank fills. Once full.... give them an hour and see if additional leaks manifest themselves.
You'll need good access to all sides of the tank, or an inspection camera to keep an eye on less accessible areas. Most likely it's fittings, and not the tank itself that's leaking.
It just takes time and perseverance, everything is fixable.
If you find a bad seal, ensure you use a solid rubber seal/oring. Do not use marine silicone sealant as it will likely fail in short order. Silicone doesn't adhere well to plastics. If you need a soft sealant, use one that is compatible with plastics AND that is food safe, such as CTEC CT1. It's the only product I know of that will stick to plastics, is stretchy and food safe.
Same consideration for thread sealant.... I personally prefer tape, but the are some food safe liquid thread sealants. If you have inspection ports, ensure the ring has a gasket.
You've already confirmed they are freshwater and not saltwater leaks?
Your water lines are likely 15mm with push-fit fittings. These are usually very reliable. If you have to take one of these apart, make sure you use an appropriate lubricant on the little internal o-ring before reassembly. 15mm fittings are accessible from most marine chandleries, but usually by special order only (from marine catalogues).
Tanks are removable. I'd be surprised if there are any fittings underneath the tanks. Usually, they are on the sides (drains) or tops (feed). If you suspect a leak underneath a tank you can't access, you may have to create an inspection port to make repairs. For integral tanks, you can either repair or fit them with internal bladders.
Hunters from that era are generally very well designed in terms of having access to service items. Take your time, take lots of photos as you take things apart. Sometimes a small mirror is helpful for finding fasteners that are hidden around a corner. The more empty the boat is, the easier it will be to work. If you can, remove all the cushions from the boat.
Likely you have more than one leak. Fix one, and you'll be able to trace down the others.... good luck. Don't try to fix everything at once, you'll go completely mental!
