Sounds like neutral safety switch to me. But yes, there is the possibility that the lanyard/kill switch (which ALL BOATS SHOULD HAVE), could have an open wire failure to only 1 of the two ingitions.

I recently fixed a boat where every time the port side Throttle was shifted into gear, one of the wires for the NSS on the Throttle was getting pinched. Finally after enough times getting pinched it broke

I don't think neutral safety switch will kill power in KOEO position, just won't allow power to starter solenoid when the key is turned to start position. The lanyard however WILL kill power to KOEO position.

Not trying to hijack but mine has 2 kill switches and now I am wondering if I should switch to a single? I am assuming that things could go bad quickly if one engine just stopped running during a wot run? Is it possible with a single kill switch used in a twin installation to allow one to start and not the other? I am assuming OP checked the ignition breaker?

Probably doesn't much matter.. If you go in the drink or kiss the nonskid, they'll both pop off..
The real question is... are you gonna wear the lanyard?? I'd guess less than 1% of people put that thing on their wrist

Surprisingly, the Cig TG strait bottoms I've been in actually had one for each engine.

Yes, you should still get power to the dash if its in gear or if the kill switch is activated.

Need to get a multi meter and start checking for voltage

My kill switch only kills the ignition. Both motors still turn over, they just don't fire. But they are not fuel injected or any of that other fancy stuff.

Had this happen to me once, turned out to be bad battery connection to the starter.

Leave the keys on and go to the fuse box in the boat usually in the cuddy but dont know what boat you have. Wiggle each fuse back and forth and up and down and see if you get alarm sound. If so pull fuse and replace . Before you insert new fuse slightly bend the spades. If its a no go flip the fuse 180 degrees and try again. Sometimes with that much power going through it sort of corrodes the receptacle so fiddling with the fuse is diagnostic
Chris