Here is my experience (we had a 1983), and then I will try to find the thread where this was discussed in great detail.
1) The plastic cover over the access to the manual bilge pump, and the rubber seal around same, and the screws holding in the rim around the whole apparatus, are all suspect. My plastic cover was cracked, the rubber was degraded, and the screws needed to be bedded with butyl tape.
If water comes in at this location, it drops down to the lazerette, which communicates freely with everything below it. The laz is not a closed box.
2) Our cockpit had a custom screen enclosure. The panels zipped into the bimini, and attached at the coaming with standard rotating tab fittings. Those fitting were screwed into the coaming, and all needed bedding with butyl tape. There were about 40. This may not apply to you.
Edit: Your bimini hardware should be properly bedded though.
3) On our boat, the starboard cockpit scupper drain (the part below the plane of the cockpit floor) was a fiberglass tube and could not leak. However, the port side scupper drain was a fitting that attached to the hose in the aft quarterberth. That fitting passed through (in order from top to bottom) the cockpit floor, and airspace of about an inch, and the false ceiling above the quarter berth. In our case the fitting was not properly bedded, and was allowing water under itself, which flowed down the fitting into the airspace, then flowed unseen across the "top" of the quarterberth ceiling toward the wooden bulkhead that separates the quarterberth from the deep starboard storage area. I changed the fitting, bedded it correctly, and used thickened epoxy to build a waterproof tunnel for the fitting to pass through what was no longer airspace.
This one was tough to find, and needed a borescope camera to confirm. More detail is in the thread, if I can find it.
4) The lids to the three cockpit lazerettes are not waterproof. If the wind and rain combine correctly, water will flow around the back side of a lid and make entry. This was particularly true for us relative to the aft laz lid on the starboard side. We kept originally kept PFDs in that location, and they were almost always wet.
5) Your steering pedestal may be leaking.
I hope this gives you some ideas. Chasing leaks on a sailboat is a pain, but worth it for a dry boat. I'll go look for that thread.
This is one thread, but I'm looking for another:
Found wet fabric at the very aft end of the quarter berth (1986 H31). This is usually a dark, damp area with no ventilation, but the water was very noticeable when I peeled up the fabric. I checked the port side cockpit drain hose that exits in this area, but found no leaks. I have checked all...
forums.sailboatowners.com
Found it! It's long, but worth a read:
Just bought a 1984 Hunter 31. Spent a week now throwing 8 garbage bags of junk from the boat, two days of hull cleaning and locker emptying and cleaning and now starting massive interior cleanup. Found after raining 5 of the ports leak, but thats ok, I know where the leak is and what needs to be...
forums.sailboatowners.com
Unfortunately, some of the information that I recall being in the thread was probably in various PMs I exchanged with various folks in the thread. The title relates to a leak in the area of the fuel tank, but on page 2 takes a turn toward another area of leakage. There is also a post that talks about the laz lids not being watertight.