1984 70hp Johnson. Very bizarre electrical issue! Need help!

As stated above, I own a 1984 Johnson 70. This motor has been a workhorse! However, here recently I’ve run into an an issue that has be stumped. While on the water, the motor runs great, however, if I encounter rough water for an extended period of time the motor will suddenly stall out. Once the motor dies there is absolutely no chance of getting it to come back on. Gas tank checked, fuel lines checked, fuel connections checked. It does not appear to be a fuel issue, seeing as how the motor does not fire at all! This is where it gets weird, once I get the motor back home and it sits up for roughly one day, the motor fires right up with no issue whatsoever. In particular, the motor will start running as soon as it’s completely dry, leading me to believe something is grounding out perhaps. In the end I’m no mechanic and don’t have the money to start throwing new parts on. Any insight or redirection will be greatly appreciated!

If you're caught in a bad natured following sea whereas waves are breaking over the engine, water is eventually going to be drawn into the fuel area (carburetor throats). If this is the case, yeah... it would take a good days length of time to dry out. And again, if this is the case, you're lucky that you don't have a bunch of rusty parts.

Putting the above aside for the time being as not happening and as you suspect, the problem is ignition. The real test would be to do a spark test after the engine fails and will not restart... however, for the moment, do the following spark test to see what you have now.
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(Spark Test)
With all of the spark plugs removed, rig a spark tester so that the spark has a 7/16" gap to jump. The spark should jump that 7/16" gap with a strong blue lightning like flame... a real SNAP! Does it?
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No tester?... Build The Following)
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(Spark Tester - Home Made)
(J. Reeves)

You can use a medium size philips screwdriver (#2 I believe) inserted into the spark plug boot spring connector, then hold the screwdriver shank approximately 7/16" away from the block to check the spark or build the following:

A spark tester can be made with a piece of 1x4 or 1x6, drive a few finishing nails through it, then bend the pointed ends at a right angle. You can then adjust the gap by simply twisting the nail(s). Solder a spark plug wire to one which you can connect to the spark plug boots, and a ground wire of some kind to the other to connect to the powerhead somewhere. Use small alligator clips on the other end of the wires to connect to ground and to the spark plug connector that exists inside of the rubber plug boot.

Using the above, one could easily build a spark tester whereas they could connect 2, 4, 6, or 8 cylinders all at one time. The ground nail being straight up, the others being bent, aimed at the ground nail. A typical 4 cylinder tester follows:

..........X1..........X2

.................X..(grd)

..........X3..........X4

This can obviously be modified to a 6 or 8 cylinder setup tester.
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Let us know what you find.

Run with a timing light hooked up.-----See if it is an ignition problem when motor falters.-------If ignition is good then fuel issues are possible.----Then again it could just be an electrical problem with wires touching ground somewhere.