The radio was something I mentioned because that's how I have my setup. The charger is constantly on, holding my battery at 13.8V. The radio plays off the battery. If there was no battery the radio would play off the charger but it would play horribly. The TS mentioned his load was some LED's. We haven't discussed the load because that's not a part of the question other than it's a load.the radio power feed

A depletion mode P-mosfet will be on when its gate floats, it still conducts from source to drain with no voltage on the gate.Both gates float (not at zero volts) and the D mode FET turns off and the E mode FET turns ON.
That would certainly be a valid scheme, it will work. AND it could be implemented with just one counter IC like the CD4060, and one transistor to drive the relay. And the timer would not even need to be really accurate, four minutes will be just as good as five!!How about a timer circuit that is generating say a one second pulse every 5 minutes. this pulse would break the drive to the relay coil. When the charger supply was removed the relay would remain latched until the next pulse occured. This would remove the back feed from the battery so there would then be no power to the relay coil. The timer would be powered from the charger side of the relay contact.
Les.
How? I can't see it. Not unless there's another relay controlling the main charging/load-switching relay.this pulse would break the drive to the relay coil