84 Crew Cab, strange electrical problem

[Bino]

I recently picked up a 1984 K30 Camper Special to ultimately be my DD and work truck. It's 100% original and unmolested (but lots of deferred maintenance). It has clearly not been regularly driven in quite a while. I'm pretty sure it has every option for an 84. It's a K30 with 6.2L and SM465. Recently it's had a strange battery issue, if it sits for a while, when I turn the ignition, the truck is 100% electrically dead, no headlights, no brake lights, no starter click, nothing. I have a manual glow plug switch that does work, however, I can hear the relay click when I press it. I checked the batteries and they both have 12.4V, so they're fine. If I put a charger on the batteries for less than a minute, the truck will miraculously come to life. The batteries and alternator are fairly new. Any thoughts? Thanks.