The yellow wire (memory, clock, etc) is wired to the constant unswitched 12v from the battery. The Red wire (accessory) is wired through the relay contact and is only under power when the ignition is on. No different than if in a truck with an accessory lead off of the ignition switch. The relay is acting as your ignition accessory lead for the radio. As far as battery size.... I would think something like a small motorcycle battery or a sealed lead acid battery similar to what is used in UPS's would suffice like a 12v 15AH. The Amp Hour rating on a battery means thats how long it can provide current (in hours) when a constant 1 amp draw is applied to it before it is drained. It's just a standard of measure for battery ratings. The current draw for the yellow lead is very small, somewhere in the low milliamp range. Without knowing the exact current draw, which you could measure to find out, and how long you leave the truck sitting at times will all factor in. I see you are my neighbor to the north. If you leave it set all winter in the cold, it may or may not be dead come spring, hard to know. During the rest of the year with occassional driving it would hold a charge just fine. In my schematic the voltage booster is off and not adding to the battery draw down when the truck isn't running. The only draw on the battery at that time is the miniscule amount the radio needs for memory functions. The sealed lead acid battery like what's used in a UPS would work well if you were to put it under the seat of the truck. They can be had at places like batteriesplus for $20-$30 give or take. I hope this helps!
