A fuse that blows randomly is caused by one of two things:
- A solid short that occurs randomly
- A steady building load that needs just one more little thing added to exceed the fuse rating
Were it my truck, I would build some gadget that would allow me to connect an ammeter in series with the fuse. If the reading was at a comfortably low level with all the items on that branch running, I would suspect cause #1. If the load was at some continual high level so that any added load would blow the fuse, that would be cause #2.
Depending on the type of your aftermarket radio, and your particular listening habits, that could be the issue. Some aftermarket radios could be more of a current hog than the stock radio. If you like to play it loud, with boomy bass, that would cause current spikes that might blow the fuse. This would fall under cause #2.
If you have an intermittent solid short- a cracked or cut wire that occasionally touches chassis metal- good luck. Stuff like that is notoriously difficult to find. Best approach is to try to isolate the different branches then get in there with an ohmmeter and start wiggling wires, and use a magnifying glass for visual inspection.
I assume we're still talking about fuse #1. Looking at the wiring diagram, there's a lot of places this circuit goes- the door switches for the interior lighting, the main (headlight) switch for the courtesy light switch there, the dome light, the glove box light, and the cargo box light on the rear outside of the cab. This all in addition to the radio power.
You mentioned the parking brake. The brake warning lights are associated with fuses 5 and 7, not likely to cause a problem on fuse circuit #1.